A Comparative Analysis of Overnight vs. Daytime Static and Momentum Strategies Across Sector ETFs

Abstract

This study examines overnight vs. daytime static and momentum strategies applied to ten sector Exchange-traded funds (ETFs) over a 27-year period from 1999 to 2025. Our findings reveal that several such strategies, particularly reversal strategies, consistently outperform static and buy-and-hold strategies. This outperformance decreases significantly when transaction costs are taken into account. We consider two transaction-cost scenarios (1 bps vs. 2 bps), which are industry standards for institutional and retail investors, respectively. We provided a detailed analysis of volatility and drawdowns. Our results indicate that by considering night and daytime separately, it is possible to outperform passive strategies for most sector ETFs.

1. Introduction

Research Question and Scope

This paper addresses a precise empirical question: does splitting the 24 h trading day into an overnight sub-period (close-to-open) and a daytime sub-period (open-to-close) generates exploitable return patterns in U.S. sector ETFs, and if so, does the alpha arise from the temporal decomposition itself or from the specific momentum or reversal signal applied to each sub-period? A result that would count as failure is one in which (i) sub-period strategies do not outperform buy-and-hold after realistic transaction costs, or (ii) applying the same signal logic to undivided 24 h returns produces comparable results, indicating that decomposition adds nothing. We test both failure conditions directly: the first through the transaction cost analysis of Section 5, Section 6, Section 7, Section 8, Section 9 and Section 10, and the second through the 24 h close-to-close strategy comparison in Section 11. Our central finding is that the first failure condition is met only for retail investors facing costs above 2–3 bps, and the second failure condition is never met—sub-period strategies generate approximately 80× more terminal wealth than equivalent 24-h strategies across all cost regimes.

This study examines the profitability of inertial trading strategies applied to ten sector Exchange-traded funds (ETFs) over a 27-year period from 1999 to 2025. We investigate multiple distinct strategies focusing on day and overnight momentum effects.

Momentum and reversal strategies are widely used in algorithmic trading. The seminal work by Jegadeesh and Titman (1993) established that buying past winners and selling past losers generates significant returns over 3–12 month horizons. The profitability of these strategies has been addressed by many authors (Carhart 1997; Daniel and Moskowitz 2016; Dobrynskaya 2019; Hanauer and Windmüller 2023; Hong and Stein 1999; Jegadeesh and Titman 2001, 2011; Kelly et al. 2021). The efficient market hypothesis Fama (1970) suggests such patterns should not persist, yet behavioral theories by De Bondt and Thaler (1985) provide explanations for momentum and reversal effects.

Predicting the direction of stock price movements has been the most difficult. The volatility of markets has traditionally prompted reliance on conventional forecasting methods such as regression analysis (Siew and Nordin 2012), exponential smoothing (de Faria et al. 2009), autoregressive integrated moving-average (ARIMA) (Ariyo et al. 2014), and technical indicators. These methods often fail to capture the complex dependencies and patterns in financial time-series data. As an alternative, deep learning-based machine learning models for stock price prediction have been proposed (Cao 2024; Kundu and Sasinthiran 2024). For detailed bibliographic references, see (Althelaya et al. 2018; Fischer and Krauss 2017; Rokhsatyazdi and Zainal 2020).

The appeal of these models is in their ability to model long-term dependencies, critical in the analysis of financial time series data, retain information and discover patterns and dependencies. However, accurately predicting stock price direction has proven difficult, even with advanced models. In a recent study (Kundu and Pinsky 2025), several deep learning architectures were used to predict the daily directions for the same 10 Sector ETFs considered in this paper. It was found that after taking trading costs into account, there is limited value from deep learning in predicting daily price movements for most stocks. The only exceptions were the Technology and Consumer Durables sectors. In related work (Zhang and Pinsky 2025b), LSTM-based deep learning architectures were used to predict the direction of daytime and overnight prices for S&P-500 and Nasdaq-100 ETFs. It was found that ignoring transaction costs and combining “overnight” and “daytime” strategies, LSTM delivers about 40% more return than passive buy-and-hold. At the same time, it is computationally expensive, requiring a full year of training for each overnight and daytime prediction. In this work, we split the 24-h period into separate sub-periods (overnight and daytime) for sector ETFs. Our results use very simple trading strategies for overnight and daytime periods and deliver significantly better results across most sectors than LSTM results in the work of Zhang and Pinsky (2025b).

The overnight return phenomenon, where a significant portion of equity returns is earned during non-trading hours, has been documented extensively (Berkman et al. 2012; Kelly and Clark 2011; Lou and Polk 2022; Lou et al. 2019; Zhang and Pinsky 2025b). A detailed study of overnight gaps is presented in Arratia and Dorador (2019). Several models were analyzed, including regime-change and autoregressive models.

In addition to challenges in modeling daytime and overnight pricing behavior, transaction costs represent a critical factor in strategy viability, as demonstrated by recent research showing that many documented anomalies disappear after accounting for realistic trading frictions (Amihud 2002; Frazzini et al. 2018; Korajczyk and Sadka 2004; Lesmond et al. 2004; Novy-Marx and Velikov 2016).

A related but underexplored dimension is the timing of entry and exit decisions under uncertainty and cost constraints. Arratia & Dorador (Arratia and Dorador 2019) studied the efficacy of stop-loss rules in the presence of overnight gaps, a setting closely related to ours. More broadly, optimal stopping theory provides a rigorous framework for deciding when to trade and when to stay out given transaction costs and uncertainty about future returns. Recent work in energy and commodity markets—including cost-aware entry rules for carbon emission rights Gallego-Alvarez et al. (2016)—demonstrates that timing decisions under cost uncertainty share the same fundamental structure as the sub-period entry decisions we study here: an agent must decide at each close whether the expected overnight return justifies the round-trip transaction cost. This framing sharpens our viability thresholds: the 1–2 bps breakeven documented in Section 5 is precisely the optimal stopping boundary below which entry is rational and above which staying in cash dominates.

In this work, we focus on simple overnight and daytime strategies using S&P sector Exchange-traded funds. Exchange-traded funds have grown dramatically as investment vehicles (Lettau and Madhavan 2018), enabling cost-effective implementation of sector-based strategies, though concerns about their market impact have been raised (Ben-David et al. 2018; Israeli et al. 2017). Industry and sector momentum effects have been documented (Fama and French 1997; Moskowitz and Grinblatt 1999), motivating our sector-level analysis.

This research analyzes nine major sector ETFs representing diverse economic segments of the U.S. market, as well as the broad market represented by the SPY ETF. These are:

1.

SPY (benchmark S&P 500 index)

2.

XLB (Materials)

3.

XLE (Energy)

4.

XLF (Financials)

5.

XLI (Industrials)

6.

XLK (Technology)

7.

XLP (Consumer Staples)

8.

XLU (Utilities)

9.

XLV (Healthcare)

10.

XLY (Consumer Discretionary)

These ETFs provide a comprehensive view of the U.S. market, allowing us to examine how momentum effects vary across different economic sectors with distinct risk–return characteristics during overnight and daytime sub-periods. Our results for these sector ETFs should be viewed in a larger context. Most stocks do not exist in isolation but belong to some sector, represented by a corresponding sector ETF. Extensive analysis in Kundu and Pinsky (2025) shows that sector ETFs accurately reflect the directional movements of their component stocks. Therefore, we can replace the analysis of an individual stock with that of its typical “sector” stock, represented by an ETF. Therefore, our results could be used to assess the relative profitability of suggested strategies for individual stocks as well.

This paper is organized as follows: Section 2 describes the methodology and computation of returns, including an autocorrelation analysis of sub-period returns in Section 2 that motivates the choice of strategies over ARIMA-based alternatives. Section 3 describes the strategies in detail with formulas for computing returns and numerous examples. Section 4 discusses the comparative performance of strategies focusing on growth. Section 5 discusses the impact of transaction costs for strategies across different ETFs, showing that at 1 bp (institutional standard), 13 of 240 strategy-ETF combinations remain profitable, while at 2 bps, only 7 survive. Section 6 compares the Sharpe ratios. Section 7 focuses on volatility comparison between strategies. Section 8 compares maximum drawdowns. Section 9 presents aggregate performance metrics averaged across all ten ETFs, whereas Section 10 focuses on strategy classification by trading intensity and provides an overall comparison between strategies. Finally, Section 11 provides some concluding remarks and suggestions for future research.

Additional tables and analysis are presented in the Appendix A, Appendix B, Appendix C, Appendix D, Appendix E, Appendix F, Appendix G, Appendix H and Appendix I. Appendix A summarizes formulae for returns for all strategies. Appendix B contains tables on total and daily transaction statistics. Appendix C compares strategies by efficiency that reflect a strategy’s ability to capture most of the returns. Appendix D presents an analogy between a trading strategy and a nearest neighbor k-NN machine learning classifier that assigns a trading label. Appendix E presents statistics of overnight and daytime returns. Appendix F presents a comparison of strategies by label prediction accuracy. Appendix G presents statistical results of a 27-year stationary bootstrap. Appendix H compares return tail statistics for daytime and overnight periods. Finally, Appendix I presents a sign pair analysis showing that lookback should be limited to a single sub-period.

2. Data and Methodology

Historical stock data for the S&P-500 and ETFs were collected from the WRDS (Wharton Research Data Services) database covering the period from 1 January 1999 to 19 December 2025 Wharton School (2024). All ten ETFs were traded continuously over the full 1999–2025 period. The nine Select Sector SPDR ETFs (XLB, XLE, XLF, XLI, XLK, XLP, XLU, XLV, XLY) were launched in December 1998, making 1 January 1999 a natural and complete start date with no initial listing gap. Prices are split- and dividend-adjusted as provided by the WRDS CRSP database, ensuring that corporate actions do not introduce artificial return discontinuities. There are no missing daily observations for any ETF; the total sample comprises $T=6782$ trading days across all ten securities.

Table 1. Example of historical stock data.

Date ${\mathit{d}}_{\mathit{i}}$	Day	Open Price ${\mathit{O}}_{\mathit{i}}$	Close Price ${\mathit{C}}_{\mathit{i}}$
1 April 2024	Monday	100.00	100.00
2 April 2024	Tuesday	110.00	95.00
3 April 2024	Wednesday	92.00	90.00
4 April 2024	Thursday	88.00	85.00
5 April 2024	Friday	90.00	95.00

provides an example of the daily open and close prices $O_i$ and $C_i$ of a hypothetical stock for trading day $d_i$.

We divide each day $d_i$ into three time periods shown in Figure 1.

For each $d_i$, let $O_i$ and $C_i$ denote the open and close prices, respectively. A day $d_i$ consists of two periods:

1.

(Previous) night period: time between the closing time of stock trading of the previous trading day $d_{i-1}$ and the opening time of the present day $d_i$

2.

Daytime period: time between the opening time of stock trading for $d_i$ and the closing time of stock trading for the same day $d_i$

For the U.S. market, the opening and closing times are the times of the main floor of the New York Stock Exchange: the opening time is 9:30 a.m. EST and the closing time is 4:00 p.m. EST. Although we do have (sometimes active) pre-market and extended hours trading, we will ignore these times and only consider the above times.

We compute the corresponding returns for each day $d_i$ and its sub-periods as follows:

1.

CC (close-to-close or “24 h” trading): the return is computed as the percent change between the close price $C_{i-1}$ of trading day $d_{i-1}$ and the close price $C_i$ of the day $d_i$. We will use the notation $R_i^{CC}$ to denote such returns. This definition corresponds to the standard definition of daily returns in finance.

2.

CO (close-to-open or “night” trading): this is the return of the first sub-period (night portion) of day $d_i$. Since this sub-period is the same as the previous night period, its return is computed as the percent change between the close price $C_{i-1}$ at $d_{i-1}$ and the open price $O_i$ of the trading day $d_i$. We will use the notation $R_i^{CO}$ to denote such returns.

3.

OC (open-to-close or “daytime” trading): this is the return of the second sub-period (daytime portion) of day $d_i$. We will use the notation $R_i^{OC}$ to denote such returns.

Note that for the CC return $R_i^{CC}$ for day $d_i$, we have:

$$R_i^{CC}=\left[1+R_i^{CC}\right]-1={\displaystyle \frac{C_i}{C_{i-1}}}-1=\left[{\displaystyle \frac{O_i}{C_{i-1}}}\right]·\left[{\displaystyle \frac{C_i}{O_i}}\right]-1=\left[1+R_i^{CO}\right]·\left[1+R_i^{OC}\right]-1$$

(1)

The 24 h return $R_i^{CC}$ is the compounded return from the night and day sub-periods ($R_i^{CO}$ and $R_i^{OC}$), as expected.

From the initial close and open price data in Table 1, we compute the return data for the three periods. An example is given in

Table 2. Example of historical stock data with % returns.

Date	Day ${\mathit{d}}_{\mathit{i}}$	Prices		Returns
		Open	Close	${\mathit{R}}_{\mathit{i}}^{\mathit{CO}}$	${\mathit{R}}_{\mathit{i}}^{\mathit{OC}}$	${\mathit{R}}_{\mathit{i}}^{\mathit{CC}}$
		${\mathit{O}}_{\mathit{i}}$	${\mathit{C}}_{\mathit{i}}$	Night	Day	24-h
4 January 2024	Monday	100.00	100.00	0.00	0.00	0.00
4 February 2024	Tuesday	110.00	95.00	10.00	−13.64	−5.00
4 March 2024	Wednesday	92.00	90.00	−3.16	−2.17	−5.26
4 April 2024	Thursday	88.00	85.00	−2.22	−3.41	−5.55
4 May 2024	Friday	90.00	95.00	5.88	5.56	11.76

.

Autocorrelation Structure of Sub-Period Returns

A natural preliminary question before specifying any momentum or reversal strategy is whether the sub-period return series exhibit serial dependence, and, if so, of what sign and at what lags. We compute the sample autocorrelation function (ACF) for the overnight ($R^{CO}$), daytime ($R^{OC}$), and full 24 h ($R^{CC}$) return series for all ten ETFs over the complete 1999–2025 sample, retaining lags 1 through 20. Significance bounds are drawn at the conventional $\pm 1.96/\sqrt{T}$ level, where $T=6782$ trading days, giving a 95% confidence interval of $\pm 0.024$.

The key numerical findings are summarized in Figure 2 for SPY (three panels: overnight, daytime, and 24-h) and in Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7 for all ten ETFs in side-by-side overnight/daytime format.

Lag-1 autocorrelation: Across all ten ETFs and all three sub-period definitions, the lag-1 autocorrelation is uniformly negative (

Table 3. Lag-1 autocorrelation and Ljung–Box test (lag 10) for all ETFs.

	Overnight ${\mathit{R}}^{\mathit{CO}}$			Daytime ${\mathit{R}}^{\mathit{OC}}$			24-h ${\mathit{R}}^{\mathit{CC}}$
ETF	ACF(1)	LB-Q(10)	p-Value	ACF(1)	LB-Q(10)	p-Value	ACF(1)	LB-Q(10)	p-Value
SPY	$-0.093$	significant	<0.001	$-0.067$	significant	<0.001	$-0.083$	significant	<0.001
XLB	$-0.050$	significant	<0.001	$-0.030$	significant	0.035	$-0.034$	significant	<0.001
XLE	$-0.061$	significant	<0.001	$-0.069$	significant	<0.001	$-0.046$	significant	0.008
XLF	$-0.077$	significant	<0.001	$-0.118$	significant	<0.001	$-0.095$	significant	<0.001
XLI	$-0.039$	significant	<0.001	$-0.046$	significant	<0.001	$-0.035$	significant	<0.001
XLK	$-0.074$	significant	<0.001	$-0.082$	significant	<0.001	$-0.069$	significant	<0.001
XLP	$-0.033$	significant	<0.001	$-0.025$	not sig.	0.081	$-0.077$	significant	<0.001
XLU	$-0.017$	not sig.	<0.001	$-0.032$	significant	0.002	$-0.078$	significant	<0.001
XLV	$-0.041$	significant	<0.001	$-0.027$	significant	0.011	$-0.034$	significant	<0.001
XLY	$-0.027$	significant	0.003	$-0.014$	not sig.	0.091	$-0.027$	significant	0.001

95% confidence interval: $\pm 0.024$. LB-Q(10) = Ljung–Box portmanteau statistic at lag 10.

). For overnight returns, the values range from $-0.017$ (XLU) to $-0.093$ (SPY), while for daytime returns, the range is $-0.014$ (XLY) to $-0.118$ (XLF). The Ljung–Box portmanteau statistic computed at lag 10 is significant ($p<0.05$) for every series except XLP daytime ($p=0.081$) and XLY daytime ($p=0.091$), indicating that short-horizon serial dependence is present across nearly all ETF-sub-period combinations. The 24 h series exhibit the same negative sign in every case, with lag-1 ACFs ranging from $-0.027$ (XLY) to $-0.095$ (XLF).

Decay structure and absence of ARIMA dynamics: A necessary condition for an ARMA$(p,q)$ or integrated process to add predictive value is that the ACF should decay slowly (geometric decay for an AR, sinusoidal for an MA, or exhibit a unit-root signature). The figures show decisively that no such structure is present: the ACF attains its most negative value at lag 1 and then decays rapidly to noise-level amplitudes by lags 2–3 in every series. The partial ACF similarly cuts off after lag 1. This pattern is the signature of a near-white-noise process with a single mild negative autocorrelation at the first lag, well described by an MA(1) or, more simply, a one-period mean-reverting shock, rather than by a long-memory or integrated process. Accordingly, fitting an ARIMA model to these series would yield an estimated AR order of zero and an MA(1) coefficient of approximately $+{\widehat{\rho }}_1\approx +0.02$ to $+0.09$, providing a negligible improvement over a driftless random walk for directional prediction purposes. We therefore do not pursue ARIMA-based strategies in this study, and instead exploit the documented static drift (overnight positive mean) and the cross-period sign asymmetry described in Appendix I.

Economic interpretation: The negative sign of ${\widehat{\rho }}_1$ is economically informative in a secondary sense. For overnight returns, a small but reliably negative autocorrelation indicates that an unusually large positive gap opening tends to be followed by a slightly smaller positive (or even negative) gap on the next trading day, consistent with a mild price-pressure reversal mechanism. For daytime returns, the pattern suggests that strong intraday moves exhibit mild mean reversion in the next session. Crucially, these first-order autocorrelations are measured over the same sub-period type across successive days (overnight-to-overnight, or daytime-to-daytime). The reversal strategies studied here instead exploit a within-day cross-period pattern: the tendency for overnight direction to reverse during the subsequent daytime session within the same 24 h cycle. This cross-period reversal is documented through the sign-pair frequency analysis in Appendix I and constitutes the principal mechanism underlying Strategy #18 (Long, Reversal).

3. Strategies

This paper examines ETF trading strategies by investing in either the night or the day portion (sub-period) of the 24 h period. We will distinguish between three types of sub-period strategies:

1.

Static—in these strategies, we always take the same position in each sub-period, independent of the performance of preceding sub-periods.

2.

Dynamic—in these strategies, we believe that the movement in the sub-period will continue (“inertia”) or reverse (“counter inertia”) in the next sub-period.

3.

Mixed—we use a static strategy on one sub-period and a dynamic strategy on another one.

We find it convenient to introduce the following notation for daily strategies. We indicate a daily strategy as a pair of sub-period strategies $(overnight,daytime)$ where $overnight$ and $daytime$ can be one of the following: Cash, Long, Short, Inertia, and Reversal (momentum):

1.

Night inertia: take a long (short) position overnight if the return for the preceding daytime period was non-negative (negative)

2.

Night reversal: take a long (short) position overnight if the return for the preceding daytime period was negative (non-negative)

Reversal:

1.

Daytime inertia: take long (short) position daytime if the return for the preceding night period was non-negative (negative)

2.

Daytime reversal: take a long (short) position daytime if the return for the preceding night period was negative (non-negative)

Therefore, there are $5\times 5=25$ possible combinations for strategies. Excluding the trivial (Cash, Cash) strategy, there are 24 strategies to consider. For each of these strategies, we are always invested in at least one sub-period. The decision to invest during the daytime or overnight is governed by the corresponding strategies. Each of the 24 strategies assumes daily rebalancing with full capital allocation and reinvestment of all returns. Final balance $B_i$ for each day is calculated using strategy return $R_i$ and the previous day’s balance $B_{i-1}$ with the following formula:

$$B_i=(1+R_i)\times B_{i-1}$$

(2)

Finally, for convenience, let us define a “sign” function $s\left(x\right)$ for any real x as follows:

$$s\left(x\right)=\left\{\begin{array}{cc}+1\hfill & x\ge 0\hfill \\ -1\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(3)

We now consider these strategies.

Static Strategies

We start with static strategies. Recall that, in these, we take long or short positions for either a daytime or overnight regardless of the movement in the previous sub-period. We use the notation $R_i$ to denote the 24 h return of a strategy for day $d_i$.

• Single Sub-period Static Strategies:
  • (Long, Cash): always buy at the close and sell the next morning. The return $R_i=R_i^{CO}$
  • (Short, Cash): always sell short at the close and buy the next morning. $R_i=-R_i^{CO}$
  • (Cash, Long): always buy at the open and sell at the close. The return $R_i=R_i^{OC}$
  • (Cash, Short): always sell short at the open and buy at the close. The return $R_i=-R_i^{OC}$
  Examples of these strategies are shown in Table 4.
• Night and Day Combined Static Strategies:

  5.

  (Long, Long): Always stay in a long position. This is analogous to the Buy-and-Hold strategy. There is no trading. For each day, the return $R_i=(1+R_i^{CO})(1+R_i^{OC})-1$

  6.

  (Short, Short): Always stay in a short position. This is the opposite of the Buy-and-Hold strategy. There is no trading. For each day, the return $R_i=(1-R_i^{CO})(1-R_i^{OC})-1=-R_i^{CC}$

  7.

  (Short, Long): Switch to a short position for the overnight sub-period and then switch to a long position for the daytime sub-period. The return $R_i=(1-R_i^{CO})(1+R_i^{OC})-1$

  8.

  (Long, Short): Switch to long position for the overnight sub-period and then switch to short position for the daytime sub-period. The return is $R_i=(1+R_i^{CO})(1-R_i^{OC})-1$

  Examples of these strategies are shown in Table 5.
• Single Sub-Period Inertia/Reversal Strategies:

  9.

  (Cash, Inertia): In this momentum strategy, you believe that the stock will continue its daytime movement in the same direction as its overnight movement. We do not have overnight positions and hold positions only during the daytime. The return $R_i=s\left(R_i^{CO}\right)R_i^{OC}$

  10.

  (Cash, Reversal): In this reversal strategy, you believe that the stock will reverse its overnight direction during the daytime We do not have overnight positions and hold positions only during the daytime. The return $R_i=-s\left(R_i^{CO}\right)R_i^{OC}$

  11.

  (Inertia, Cash): In this strategy, you believe that the stock will continue its overnight movement for $d_i$ in the same direction as it did during the overnight. We have no daytime positions. The return $R_i=s\left(R_{i-1}^{OC}\right)R_i^{CO}$

  12.

  (Reversal, Cash): In this strategy, you believe that the stock will reverse its daytime direction during the next night sub-period. We have no daytime positions. The return $R_i=-s\left(R_{i-1}^{OC}\right)R_i^{CO}$

  These four strategies are shown in Table 6.
• Combined Inertia/Reversal Strategies:

  13.

  (Inertia, Inertia): $R_i=[1+s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1+s\left(R_i^{CO}\right)R_i^{OC}]-1$

  14.

  (Inertia, Reversal): $R_i=[1+s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1-s\left(R_i^{CO}\right)R_i^{OC}]-1$

  15.

  (Reversal, Inertia): $R_i=[1-s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1+s\left(R_i^{CO}\right)R_i^{OC}]-1$

  16.

  (Reversal, Reversal): $R_i=[1-s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1-s\left(R_i^{CO}\right)R_i^{OC}]-1$

  These four strategies are shown in Table 7.
• Static Night and Daytime Inertia/Reversal Strategies:

  17.

  (Long, Inertia): $R_i=[1+R_i^{CO}]·[1+s\left(R_i^{CO}\right)R_i^{OC}]-1$

  18.

  (Long, Reversal): $R_i=[1+R_i^{CO}]·[1-s\left(R_i^{CO}\right)R_i^{OC}]-1$

  19.

  (Short, Inertia): $R_i=[1-R_i^{CO}]·[1+s\left(R_i^{CO}\right)R_i^{OC}]-1$

  20.

  (Short, Reversal): $R_i=[1-R_i^{CO}]·[1-s\left(R_i^{CO}\right)R_i^{OC}]-1$

  These four strategies are shown in Table 8.
• Night Inertia/reversal and Daytime Static Strategies:

  21.

  (Inertia, Long): $R_i=[1+s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1+R_i^{OC}]-1$

  22.

  (Reversal, Long): $R_i=[1-s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1+R_i^{OC}]-1$

  23.

  (Inertia, Short): $R_i=[1+s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1-R_i^{OC}]-1$

  24.

  (Reversal, Short): $R_i=[1-s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1-R_i^{OC}]-1$

Table 4. Examples of single sub-period static strategies.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
1	(Long, Cash)	cash	cash	long	cash	long	cash	long	cash	long	cash
2	(Short, Cash)	cash	cash	short	cash	short	cash	short	cash	short	cash
3	(Cash, Long)	cash	cash	cash	long	cash	long	cash	long	cash	long
4	(Cash, Short)	cash	cash	cash	short	cash	short	cash	short	cash	short

Table 4. Examples of single sub-period static strategies.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
1	(Long, Cash)	cash	cash	long	cash	long	cash	long	cash	long	cash
2	(Short, Cash)	cash	cash	short	cash	short	cash	short	cash	short	cash
3	(Cash, Long)	cash	cash	cash	long	cash	long	cash	long	cash	long
4	(Cash, Short)	cash	cash	cash	short	cash	short	cash	short	cash	short

Table 5. Examples of combined static strategies.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
5	(Long, Long)	cash	cash	long	long	long	long	long	long	long	long
6	(Short, Short)	cash	cash	short	short	short	short	short	short	short	short
7	(Short, Long)	cash	cash	short	long	short	long	short	long	short	long
8	(Long, Short)	cash	cash	long	short	long	short	long	short	long	short

Table 5. Examples of combined static strategies.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
5	(Long, Long)	cash	cash	long	long	long	long	long	long	long	long
6	(Short, Short)	cash	cash	short	short	short	short	short	short	short	short
7	(Short, Long)	cash	cash	short	long	short	long	short	long	short	long
8	(Long, Short)	cash	cash	long	short	long	short	long	short	long	short

Table 6. Examples of single sub-period static strategies.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
9	(Cash, Inertia)	cash	cash	cash	long	cash	short	cash	short	cash	long
10	(Cash, Rev.)	cash	cash	cash	short	cash	long	cash	long	cash	short
11	(Inertia, Cash)	cash	cash	cash	cash	short	cash	short	cash	short	cash
12	(Rev, Cash)	cash	cash	cash	cash	long	cash	long	cash	long	cash

Table 6. Examples of single sub-period static strategies.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
9	(Cash, Inertia)	cash	cash	cash	long	cash	short	cash	short	cash	long
10	(Cash, Rev.)	cash	cash	cash	short	cash	long	cash	long	cash	short
11	(Inertia, Cash)	cash	cash	cash	cash	short	cash	short	cash	short	cash
12	(Rev, Cash)	cash	cash	cash	cash	long	cash	long	cash	long	cash

Table 7. Examples of combined inertia/reversal.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
13	(Inertia, Inertia)	cash	cash	cash	long	cash	short	cash	short	cash	long
14	(Inertia, Reversal)	cash	cash	cash	short	cash	long	cash	long	cash	short
15	(Reversal, Inertia)	cash	cash	cash	cash	long	cash	long	cash	long	cash
16	(Reversal, Reversal)	cash	cash	long	short	long	long	long	long	long	short

Table 7. Examples of combined inertia/reversal.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
13	(Inertia, Inertia)	cash	cash	cash	long	cash	short	cash	short	cash	long
14	(Inertia, Reversal)	cash	cash	cash	short	cash	long	cash	long	cash	short
15	(Reversal, Inertia)	cash	cash	cash	cash	long	cash	long	cash	long	cash
16	(Reversal, Reversal)	cash	cash	long	short	long	long	long	long	long	short

Table 8. Examples of static night and dynamic daytime inertia/reversal.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
17	(Long, Inertia)	cash	cash	long	long	long	short	long	short	long	long
18	(Long, Reversal)	cash	cash	long	short	long	long	long	long	long	short
19	(Short, Inertia)	cash	cash	short	long	short	short	short	short	short	long
20	(Short, Reversal)	cash	cash	short	short	short	long	short	long	short	short

Table 8. Examples of static night and dynamic daytime inertia/reversal.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
17	(Long, Inertia)	cash	cash	long	long	long	short	long	short	long	long
18	(Long, Reversal)	cash	cash	long	short	long	long	long	long	long	short
19	(Short, Inertia)	cash	cash	short	long	short	short	short	short	short	long
20	(Short, Reversal)	cash	cash	short	short	short	long	short	long	short	short

These four strategies are shown in

Table 9. Examples of dynamic night and static daytime inertia/reversal.

#	Strategy	Monday		Tuesday		Wednesday		Thursday		Friday
		Night	Day	Night	Day	Night	Day	Night	Day	Night	Day
		$0.00$	$0.00$	$10.00$	$-13.64$	$-3.16$	$-2.17$	$-2.22$	$-3.41$	$5.88$	$5.56$
21	(Inertia, Long)	cash	cash	cash	long	short	long	short	long	short	long
22	(Reversal, Long)	cash	cash	cash	long	long	long	long	long	long	long
23	(Inertia, Short)	cash	cash	cash	short	short	short	short	short	short	short
24	(Reversal, Short)	cash	cash	cash	short	long	short	long	short	long	short

.

The formulae for computing daily returns for each strategy are summarized in

Table A1. Strategy return formulas.

#	Strategy		Sub-Period Returns		24 h Strategy Return ${\mathit{R}}_{\mathit{i}}$
	Overnight	Daytime	Overnight	Daytime
#1	Long	Cash	$R_i^{CO}$	0	$R_i^{CO}$
#2	Short	Cash	$-R_i^{CO}$	0	$-R_i^{CO}$
#3	Cash	Long	0	$R_i^{OC}$	$R_i^{OC}$
#4	Cash	Short	0	$-R_i^{OC}$	$-R_i^{OC}$
#5	Long	Long	$R_i^{CO}$	$R_i^{OC}$	$[1+R_i^{CO}]·[1+R_i^{OC}]-1$
#6	Short	Short	$-R_i^{CO}$	$-R_i^{OC}$	$[1-R_i^{CO}]·[1-R_i^{OC}]-1$
#7	Short	Long	$-R_i^{CO}$	$R_i^{OC}$	$[1-R_i^{CO}]·[1+R_i^{OC}]-1$
#8	Long	Short	$R_i^{CO}$	$-R_i^{OC}$	$[1+R_i^{CO}]·[1-R_i^{OC}]-1$
#9	Cash	Inertia	0	$s\left(R_i^{CO}\right)R_i^{OC}$	$s\left(R_i^{CO}\right)R_i^{OC}$
#10	Cash	Reversal	0	$-s\left(R_i^{CO}\right)R_i^{OC}$	$-s\left(R_i^{CO}\right)R_i^{OC}$
#11	Inertia	Cash	$s\left(R_{i-1}^{OC}\right)R_i^{CO}$	0	$s\left(R_{i-1}^{OC}\right)R_i^{CO}$
#12	Reversal	Cash	$-s\left(R_{i-1}^{OC}\right)R_i^{CO}$	0	$-s\left(R_{i-1}^{OC}\right)R_i^{CO}$
#13	Inertia	Inertia	$s\left(R_{i-1}^{OC}\right)R_i^{CO}$	$s\left(R_i^{CO}\right)R_i^{OC}$	$[1+s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1+s\left(R_i^{CO}\right)R_i^{OC}]-1$
#14	Inertia	Reversal	$s\left(R_{i-1}^{OC}\right)R_i^{CO}$	$-s\left(R_i^{CO}\right)R_i^{OC}$	$[1+s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1-s\left(R_i^{CO}\right)R_i^{OC}]-1$
#15	Reversal	Inertia	$-s\left(R_{i-1}^{OC}\right)R_i^{CO}$	$s\left(R_i^{CO}\right)R_i^{OC}$	$[1-s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1+s\left(R_i^{CO}\right)R_i^{OC}]-1$
#16	Reversal	Reversal	$-s\left(R_{i-1}^{OC}\right)R_i^{CO}$	$-s\left(R_i^{CO}\right)R_i^{OC}$	$[1-s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1-s\left(R_i^{CO}\right)R_i^{OC}]-1$
#17	Long	Inertia	$R_i^{CO}$	$s\left(R_i^{CO}\right)R_i^{OC}$	$[1+R_i^{CO}]·[1+s\left(R_i^{CO}\right)R_i^{OC}]-1$
#18	Long	Reversal	$R_i^{CO}$	$-s\left(R_i^{CO}\right)R_i^{OC}$	$[1+R_i^{CO}]·[1-s\left(R_i^{CO}\right)R_i^{OC}]-1$
#19	Short	Inertia	$-R_i^{CO}$	$s\left(R_i^{CO}\right)R_i^{OC}$	$[1-R_i^{CO}]·[1+s\left(R_i^{CO}\right)R_i^{OC}]-1$
#20	Short	Reversal	$-R_i^{CO}$	$-s\left(R_i^{CO}\right)R_i^{OC}$	$[1-R_i^{CO}]·[1-s\left(R_i^{CO}\right)R_i^{OC}]-1$
#21	Inertia	Long	$s\left(R_{i-1}^{OC}\right)R_i^{CO}$	$R_i^{OC}$	$[1+s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1+R_i^{OC}]-1$
#22	Reversal	Long	$-s\left(R_{i-1}^{OC}\right)R_i^{CO}$	$R_i^{OC}$	$[1-s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1+R_i^{OC}]-1$
#23	Inertia	Short	$s\left(R_{i-1}^{OC}\right)R_i^{CO}$	$-R_i^{OC}$	$[1+s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1-R_i^{OC}]-1$
#24	Reversal	Short	$-s\left(R_{i-1}^{OC}\right)R_i^{CO}$	$-R_i^{OC}$	$[1-s\left(R_{i-1}^{OC}\right)R_i^{CO}]·[1-R_i^{OC}]-1$

.

4. Strategy Performance Analysis

4.1. Baseline Performance Without Transaction Costs

Table 10. Final balances without transaction costs ($100 initial investment): 42 profitable. Blue color in Strategy #5 indicates the final balance for the passive Buy&Hold (long, long) strategy. The green color indicates that the corresponding strategy outperforms the passive strategy. Finally, red color indicates that the corresponding strategy underperforms the passive strategy.

#	Strategy		SPY	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY
	Overnight	Daytime
1	Long	Cash	774	1128	2378	1222	1778	3165	435	3162	1017	1001
2	Short	Cash	9	5	2	4	4	2	18	2	7	6
3	Cash	Long	98	61	30	35	49	30	123	20	76	117
4	Cash	Short	55	61	85	69	95	101	51	227	71	33
5	Long	Long	758	688	707	422	864	948	534	629	772	1169
6	Short	Short	5	3	2	3	3	2	9	6	5	2
7	Short	Long	9	3	1	1	2	0	22	0	6	7
8	Long	Short	423	685	2021	838	1681	3210	220	7189	722	331
9	Cash	Inertia	56	175	734	5	4	3	1	5	2	5
10	Cash	Reversal	95	21	3	492	1024	988	5,130	906	2217	850
11	Inertia	Cash	51	327	1769	365	206	260	20	20	122	169
12	Reversal	Cash	142	19	3	12	31	20	404	385	61	36
13	Inertia	Inertia	29	571	12,982	18	9	8	0	1	3	8
14	Inertia	Reversal	49	69	61	1795	2110	2563	1004	181	2707	1436
15	Reversal	Inertia	80	33	21	1	1	1	5	19	1	2
16	Reversal	Reversal	135	4	0	61	318	198	20,707	3486	1343	302
17	Long	Inertia	435	1974	17,458	59	80	97	5	158	25	45
18	Long	Reversal	739	239	82	6006	18,207	31,263	22,317	28,653	22,540	8513
19	Short	Inertia	5	10	16	0	0	0	0	0	0	0
20	Short	Reversal	9	1	0	18	37	16	931	22	161	51
21	Inertia	Long	50	199	525	126	100	78	24	4	93	197
22	Reversal	Long	139	11	1	4	15	6	495	76	46	41
23	Inertia	Short	28	198	1503	251	195	263	10	45	87	56
24	Reversal	Short	78	11	2	8	29	20	204	875	43	12

presents the final portfolio values for all 24 trading strategies across ten sector ETFs over the 27-year period (1999–2025), starting with $100 and assuming zero transaction costs.

Following the methodology outlined in Section 2, each strategy employs different combinations of overnight (CO: close-to-open) and daytime (OC: open-to-close) positioning, with returns compounded daily according to Equation (2). This theoretical benchmark establishes the upper bound of strategy profitability before considering implementation frictions.

Results and Discussion

Overnight vs. daytime effects: validating the core hypothesis: The results provide compelling evidence for the hypothesis that overnight periods generate stronger exploitable momentum than daytime periods. Strategy #1 (Long/Cash), which captures pure overnight returns $R_i=R_i^{CO}$, consistently outperformed across all ten ETFs with final values ranging from $435 (XLP) to $3165 (XLK). In contrast, Strategy #3 (Cash/Long), capturing pure daytime returns $R_i=R_i^{OC}$, generated losses in 8 out of 10 ETFs. This stark asymmetry contradicts the efficient market hypothesis and supports behavioral finance theories, which suggest reduced arbitrage activity during non-trading hours.

The Technology sector (XLK) exhibited the strongest overnight effect with a final value of $3165—a 3065% gain—consistent with this sector’s susceptibility to after-hours earnings announcements and international technology news. Energy (XLE) similarly achieved $2378, reflecting the sector’s exposure to 24 h global commodity markets where crude oil prices fluctuate continuously during U.S. overnight hours.

Conversely, the systematic failure of Strategy #2 (Short/Cash: $R_i=-R_i^{CO}$) across all ETFs ($2–$18 final values) demonstrates that overnight movements exhibit persistent positive drift rather than random walk behavior. If overnight returns were symmetrically distributed, short and long strategies would show comparable absolute performance, which the data clearly refute.

Decomposition of 24 h returns: static strategies: Recall from Equation (1) that the 24-h return decomposes as follows: $R_i^{CC}=(1+R_i^{CO})(1+R_i^{OC})-1$. The buy-and-hold strategy (Strategy #5: Long/Long) captures this full 24 h return with $R_i=R_i^{CC}$, achieving solid performance across most ETFs ($422–$1169). However, Strategy #1 outperformed buy-and-hold in 8 of 10 ETFs, indicating that $R_i^{CO}$ contributions dominate $R_i^{CC}$ while daytime periods often contribute negatively or minimally.

Strategy #8 (Long/Short: $R_i=(1+R_i^{CO})(1-R_i^{OC})-1$) produced exceptional results in XLU ($7189), XLK ($3210), and XLE ($2021), exploiting both positive overnight drift and negative daytime drift. This combination’s success across multiple sectors suggests that overnight gaps rarely persist into regular trading hours, consistent with profit-taking by institutional traders who entered positions overnight.

The catastrophic failure of Strategy #7 (Short/Long) across all ETFs confirms this pattern is not merely sector-specific but represents a fundamental characteristic of ETF price behavior over the study period.

Dynamic strategies: momentum vs. mean reversion: Dynamic strategies that adjust positions based on previous sub-period returns (using the sign function defined in Equation (3)) showed highly sector-dependent performance. Strategy #13 (Inertia/Inertia: $R_i=[1+s\left(R_{i-1}^{OC}\right)R_i^{CO}][1+s\left(R_i^{CO}\right)R_i^{OC}]-1$) achieved extraordinary returns in XLE ($12,982), representing a 12,882% gain over 25 years. This is consistent with Energy ETFs exhibiting stronger momentum persistence across sub-periods than other sectors; the precise mechanism warrants further investigation beyond the scope of this study.

However, the same strategy failed in most other sectors, with 7 out of 10 ETFs showing final values below $100. This heterogeneity indicates that pure momentum strategies require careful sector selection and cannot be applied universally.

Strategy #11 (Inertia/Cash: $R_i=s\left(R_{i-1}^{OC}\right)R_i^{CO}$), which uses daytime momentum signals to predict overnight movements, succeeded in XLE ($1769) and XLB ($327) but underperformed in other sectors. This pattern suggests that momentum persistence from daytime to overnight periods is strongest in commodity-linked and material sectors, where continuous global markets create information linkages across temporal segments.

Mixed strategies: optimal temporal combinations: The most consistently profitable approach across diverse sectors was Strategy #18 (Long, Reversal: $R_i=[1+R_i^{CO}][1-s\left(R_i^{CO}\right)R_i^{OC}]-1$), which maintains static long positions overnight while implementing contrarian positioning during the day based on overnight movement direction. This strategy achieved remarkable final values: XLK ($31,263), XLU ($28,653), XLV ($22,540), XLP ($22,317), XLI ($18,207), and XLY ($8513).

The success of this mixed approach validates our framework for combining static and dynamic positioning across different sub-periods. It captures reliable overnight positive drift through static long exposure while exploiting intraday mean-reversion tendencies, where gaps partially reverse during regular trading hours. The strategy’s broad applicability across six diverse sectors—spanning defensive (XLP, XLU), cyclical (XLI, XLY), growth (XLK), and healthcare (XLV)—suggests this combination addresses a fundamental market microstructure phenomenon rather than sector-specific anomalies.

Strategy #17 (Long/Inertia) showed exceptional but concentrated performance, achieving $17,458 in XLE and $1974 in XLB, but under-performing in other sectors. This concentration suggests that daytime momentum continuation after overnight gaps is particularly pronounced in commodity-sensitive sectors.

Sector heterogeneity and fundamental drivers: The substantial variation in optimal strategies across sectors reflects differences in information processing dynamics and fundamental business characteristics:

• Energy (XLE): Multiple strategies succeeded (Strategy #1: $2378; #8: $2021; #11: $1769; #13: $12,982; #17: $17,458). XLE exhibits the highest overnight return variance in all ten ETFs (

  Table A9. Summary overnight per ETF and investment sub-period.

  #	Statistics	SPY	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY
  1	$\mu (R_i^{CO}<0)$	− 0.0047	−0.0061	−0.0071	−0.0069	−0.0057	−0.0071	−0.0040	−0.0043	−0.0046	−0.0062
  2	$\mu (R_i^{CO}>0)$	0.0044	0.0058	0.0068	0.0066	0.0055	0.0067	0.0039	0.0044	0.0043	0.0058
  3	$\mu \left(R_i^{CO}\right)$	0.0003	0.0004	0.0005	0.0004	0.0005	0.0006	0.0002	0.0006	0.0004	0.0004
  4	$\sigma \left(R_i^{CO}\right)$	0.0070	0.0086	0.0102	0.0109	0.0082	0.0100	0.0059	0.0063	0.0067	0.0089
  5	$S{R}_i^{CO}$	0.0482	0.0472	0.0517	0.0393	0.0573	0.0577	0.0388	0.0882	0.0521	0.0442
  6	$MD{D}_i^{CO}$	−0.3286	−0.3834	−0.3754	−0.4593	−0.3398	−0.3575	−0.3175	−0.3438	−0.3952	−0.4799
  7	$P(R_i^{CO}\ge 0)$	0.5603	0.5836	0.5696	0.5714	0.5668	0.5866	0.5687	0.6096	0.5802	0.5745
  8	$P(R_i^{CO}<0)$	0.4397	0.4164	0.4304	0.4286	0.4332	0.4134	0.4313	0.3904	0.4198	0.4255

  ), a documented empirical property; the causal mechanism linking this to global commodity markets is a plausible but unverified hypothesis requiring further study.
• Technology (XLK): Dominated by overnight effects (Strategy #1: $3165; #8: $3210; #18: $31,263). XLK has the highest $P(R^{CO}\ge 0)$ of all ETFs (58.7%, Table A9), making it the most asymmetric sub-period return distribution—an objective basis for overnight strategy dominance in this sector.
• Utilities (XLU): Best performance from mixed strategies (Strategy #8: $7189; #18: $28,653). XLU has the highest overnight Sharpe ratio of all ETFs (0.088 vs. 0.032–0.057 for others, Table A9), a measurable empirical characteristic rather than a narrative interpretation.
• Consumer Staples (XLP): Unique reversal characteristics (Strategy #10: $5130; #16: $20,707). XLP has the highest conditional reversal probability P(daytime + | overnight −) = 55.6% (

  Table A17. Sub-period sign pair frequencies (%) and conditional reversal probabilities. P(day − | ON +) is the fraction of days on which daytime was negative given overnight was positive. Values > 50% in the conditional columns indicate a systematic reversal tendency.

  ETF	P(+,+)	P(+,−)	P(−,+)	P(−,−)	P(Day − | ON +)	P(Day + | ON +)	P(Day + | ON −)
  SPY	29.5	25.8	24.1	20.6	46.7	53.3	53.9
  XLB	29.6	26.3	21.9	22.2	47.1	52.9	49.7
  XLE	28.7	26.5	22.4	22.3	48.0	52.0	50.1
  XLF	28.9	27.1	23.9	20.1	48.4	51.6	54.3
  XLI	28.3	27.5	24.2	20.0	49.2	50.8	54.8
  XLK	29.4	27.3	23.5	19.8	48.1	51.9	54.3
  XLP	28.2	27.1	24.9	19.8	49.0	51.0	55.6
  XLU	28.4	29.1	23.0	19.6	50.6	49.4	54.1
  XLV	29.4	27.8	23.0	19.8	48.7	51.3	53.7
  XLY	30.0	26.1	23.4	20.5	46.6	53.4	53.3

  ), providing an objective quantitative basis for the reversal strategy’s success in this sector.

Implications for market efficiency: Of 240 strategy-ETF combinations, only 42 (17.5%) generated profits exceeding the initial $100 investment, with profitable strategies highly concentrated in those exploiting overnight momentum. This concentration, combined with the universal failure of all pure short strategies (Strategies #2, #6, #7, #19), provides evidence inconsistent with strong-form market efficiency. The persistent overnight drift cannot be explained by risk-based asset pricing models, as these would predict symmetric returns to long and short positions of equivalent systematic risk.

The results support the hypothesis that markets become less efficient during non-trading hours due to reduced liquidity, lower participation by professional arbitrageurs, and delayed information processing—factors that create exploitable momentum patterns. However, these theoretical results assume perfect execution at the open and close prices with zero transaction costs, which represents an upper bound on achievable performance. The following sections incorporate realistic transaction costs to assess practical viability and identify which strategies remain profitable under implementable trading conditions.

5. Transaction Cost Analysis

Table A2. Trade count analysis by strategy and ETF (total trades over 25 years).

#	Strategy		SPY	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY	Avg
	Overnight	Daytime
1	Long	Cash	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078
2	Short	Cash	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078
3	Cash	Long	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077
4	Cash	Short	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077
5	Long	Long	1	1	1	1	1	1	1	1	1	1	1
6	Short	Short	1	1	1	1	1	1	1	1	1	1	1
7	Short	Long	26,155	26,155	26,155	26,155	26,155	26,155	26,155	26,155	26,155	26,155	26,155
8	Long	Short	26,155	26,155	26,155	26,155	26,155	26,155	26,155	26,155	26,155	26,155	26,155
9	Cash	Inertia	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077
10	Cash	Reversal	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077	13,077
11	Inertia	Cash	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078
12	Reversal	Cash	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078	13,078
13	Inertia	Inertia	13,351	12,719	12,765	13,263	13,219	13,175	13,591	13,515	13,175	12,987	13,176
14	Inertia	Reversal	12,805	13,437	13,391	12,893	12,937	12,981	12,565	12,641	12,981	13,169	12,980
15	Reversal	Inertia	12,805	13,437	13,391	12,893	12,937	12,981	12,565	12,641	12,981	13,169	12,980
16	Reversal	Reversal	13,351	12,719	12,765	13,263	13,219	13,175	13,591	13,515	13,175	12,987	13,176
17	Long	Inertia	11,703	11,811	11,873	11,971	11,831	11,619	12,075	11,479	11,487	11,819	11,767
18	Long	Reversal	14,453	14,345	14,283	14,185	14,325	14,537	14,081	14,677	14,669	14,337	14,389
19	Short	Inertia	14,453	14,345	14,283	14,185	14,325	14,537	14,081	14,677	14,669	14,337	14,389
20	Short	Reversal	11,703	11,811	11,873	11,971	11,831	11,619	12,075	11,479	11,487	11,819	11,767
21	Inertia	Long	12,137	12,709	12,829	12,401	12,425	12,349	12,329	12,737	12,537	12,189	12,464
22	Reversal	Long	14,019	13,447	13,327	13,755	13,731	13,807	13,827	13,419	13,619	13,967	13,692
23	Inertia	Short	14,019	13,447	13,327	13,755	13,731	13,807	13,827	13,419	13,619	13,967	13,692
24	Reversal	Short	12,137	12,709	12,829	12,401	12,425	12,349	12,329	12,737	12,537	12,189	12,464

and

Table A3. Average trades per day by strategy and ETF.

#	Strategy		SPY	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY	Avg.
	Overnight	Daytime
1	Long	Cash	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00
2	Short	Cash	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00
3	Cash	Long	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00
4	Cash	Short	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00
5	Long	Long	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
6	Short	Short	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
7	Short	Long	4.00	4.00	4.00	4.00	4.00	4.00	4.00	4.00	4.00	4.00	4.00
8	Long	Short	4.00	4.00	4.00	4.00	4.00	4.00	4.00	4.00	4.00	4.00	4.00
9	Cash	Inertia	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00
10	Cash	Reversal	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00
11	Inertia	Cash	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00
12	Reversal	Cash	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00
13	Inertia	Inertia	2.04	1.95	1.95	2.03	2.02	2.01	2.08	2.07	2.01	1.99	2.01
14	Inertia	Reversal	1.96	2.05	2.05	1.97	1.98	1.99	1.92	1.93	1.99	2.01	1.99
15	Reversal	Inertia	1.96	2.05	2.05	1.97	1.98	1.99	1.92	1.93	1.99	2.01	1.99
16	Reversal	Reversal	2.04	1.95	1.95	2.03	2.02	2.01	2.08	2.07	2.01	1.99	2.01
17	Long	Inertia	1.79	1.81	1.82	1.83	1.81	1.78	1.85	1.76	1.76	1.81	1.80
18	Long	Reversal	2.21	2.19	2.18	2.17	2.19	2.22	2.15	2.24	2.24	2.19	2.20
19	Short	Inertia	2.21	2.19	2.18	2.17	2.19	2.22	2.15	2.24	2.24	2.19	2.20
20	Short	Reversal	1.79	1.81	1.82	1.83	1.81	1.78	1.85	1.76	1.76	1.81	1.80
21	Inertia	Long	1.86	1.94	1.96	1.90	1.90	1.89	1.89	1.95	1.92	1.86	1.91
22	Reversal	Long	2.14	2.06	2.04	2.10	2.10	2.11	2.11	2.05	2.08	2.14	2.09
23	Inertia	Short	2.14	2.06	2.04	2.10	2.10	2.11	2.11	2.05	2.08	2.14	2.09
24	Reversal	Short	1.86	1.94	1.96	1.90	1.90	1.89	1.89	1.95	1.92	1.86	1.91

in Appendix B summarize the number of transactions for each strategy. These per-trade cost figures ($\alpha$) are intended to represent all-in transaction costs, encompassing brokerage commissions, the bid-ask half-spread, and estimated market impact. For the highly liquid sector ETFs studied here—all of which rank among the most actively traded U.S. exchange-traded products, with SPY, XLK, and XLF routinely exceeding hundreds of millions of shares daily—typical institutional bid-ask spreads are below 0.5 bps and market impact for moderate position sizes is negligible. The 1 bps and 2 bps scenarios, therefore, conservatively bracket the range from large institutional (all-in $\approx 0.5$–$1.5$ bps) to smaller institutional or active-retail (all-in $\approx 2$–5 bps) cost structures, consistent with estimates reported by (Frazzini et al. 2018; Novy-Marx and Velikov 2016). For most strategies, the average number of trades per day is $k=2$. Assuming 250 trading days per year, from 1999 to 2025, we had 27 years with approximately $N=250\times 27=6750$ days. Let r denote the daily internal rate of return. Then, starting with an initial $100 investment, the final investment $B\left(str\right)$ of a strategy will be $100{(1+r)}^N$. Assume that daily trades subtract $\alpha$ from a return for every day. The compounded return after N days will be $R^{*}=r^N{(1-\alpha )}^N$. The return is reduced by ${(1-\alpha )}^N$.

Suppose $\alpha =0.01\%$ of $\alpha ={10}^{-4}$. Then, using the approximation ${(1+1/n)}^n\approx 1/e$, the loss to the return is:

$$\mathrm{Loss}={(1-\alpha )}^N={\left[{\left(1-{\displaystyle \frac{1}{\mathrm{10,000}}}\right)}^{\mathrm{10,000}}\right]}^{6750/\mathrm{10,000}}\approx {\left[{\displaystyle \frac{1}{e}}\right]}^{0.675}\approx 0.5092$$

(4)

The total return is halved. This shows that for these strategies, transaction costs play a very significant role. The effect of a 1 basis point transaction cost (typical for professional hedge funds) is illustrated in

Table 11. Final balances with 1 bp/trade transaction cost ($100 initial investment): 13 profitable. Blue color in Strategy #5 indicates the final balance for the passive Buy&Hold (long, long) strategy. The green color indicates that the corresponding strategy outperforms the passive strategy. Finally, red color indicates that the corresponding strategy underperforms the passive strategy.

#	Strategy		SPY	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY
	Overnight	Daytime
1	Long	Cash	209	305	643	330	481	856	118	856	275	271
2	Short	Cash	3	1	1	1	1	0	5	1	2	2
3	Cash	Long	26	16	8	9	13	8	33	5	21	32
4	Cash	Short	15	16	23	19	26	27	14	61	19	9
5	Long	Long	758	688	707	422	864	948	534	629	772	1169
6	Short	Short	5	3	2	3	3	2	9	6	5	2
7	Short	Long	1	0	0	0	0	0	2	0	0	1
8	Long	Short	31	50	148	61	123	235	16	526	53	24
9	Cash	Inertia	15	47	199	1	1	1	0	1	1	1
10	Cash	Reversal	26	6	1	133	277	267	1388	245	600	230
11	Inertia	Cash	14	88	478	99	56	70	5	5	33	46
12	Reversal	Cash	38	5	1	3	8	5	109	104	16	10
13	Inertia	Inertia	8	160	3610	5	2	2	0	0	1	2
14	Inertia	Reversal	14	18	16	497	581	703	286	51	742	386
15	Reversal	Inertia	22	9	5	0	0	0	1	5	0	0
16	Reversal	Reversal	36	1	0	16	85	53	5336	905	361	83
17	Long	Inertia	134	604	5307	18	24	30	2	50	8	14
18	Long	Reversal	175	57	20	1460	4365	7342	5476	6627	5218	2038
19	Short	Inertia	1	2	4	0	0	0	0	0	0	0
20	Short	Reversal	3	0	0	5	11	5	279	7	51	16
21	Inertia	Long	15	56	146	37	29	23	7	1	26	58
22	Reversal	Long	34	3	0	1	4	2	124	20	12	10
23	Inertia	Short	7	52	397	63	49	66	2	12	22	14
24	Reversal	Short	23	3	1	2	8	6	60	245	12	3

. This analysis builds on recent findings that transaction costs represent the primary barrier to exploiting documented market anomalies (Frazzini et al. 2018; Novy-Marx and Velikov 2016).

5.1. The Compounding Effect of Friction

The final balance B is a function of the gross daily return $1+r$ and the cost $\alpha$. For N days and k trades per day, the final balance is given by:

$$B=100·{\left[(1+r){(1-\alpha )}^k\right]}^N$$

(5)

When comparing the results of Table 11 (${\alpha }_1={10}^{-4}$) and

Table 12. Final balances with 2 bps/trade transaction costs ($100 initial investment)—7 profitable. Blue color in Strategy #5 indicates the final balance for the passive Buy&Hold (long, long) strategy. The green color indicates that the corresponding strategy outperforms the passive strategy. Finally, red color indicates that the corresponding strategy underperforms the passive strategy.

#	Strategy		SPY	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY
	Overnight	Daytime
1	Long	Cash	57	83	174	89	130	232	32	231	74	73
2	Short	Cash	1	0	0	0	0	0	1	0	1	0
3	Cash	Long	7	4	2	3	4	2	9	1	6	9
4	Cash	Short	4	4	6	5	7	7	4	17	5	2
5	Long	Long	758	688	706	422	864	948	533	629	772	1169
6	Short	Short	5	3	2	3	3	2	9	6	5	2
7	Short	Long	0	0	0	0	0	0	0	0	0	0
8	Long	Short	2	4	11	4	9	17	1	38	4	2
9	Cash	Inertia	4	13	54	0	0	0	0	0	0	0
10	Cash	Reversal	7	2	0	36	75	72	376	66	162	62
11	Inertia	Cash	4	24	129	27	15	19	1	1	9	12
12	Reversal	Cash	10	1	0	1	2	1	30	28	4	3
13	Inertia	Inertia	2	45	1004	1	1	1	0	0	0	1
14	Inertia	Reversal	4	5	4	137	160	193	82	15	203	104
15	Reversal	Inertia	6	2	1	0	0	0	0	2	0	0
16	Reversal	Reversal	9	0	0	4	23	14	1375	235	97	23
17	Long	Inertia	42	185	1613	5	7	9	0	16	2	4
18	Long	Reversal	41	14	5	355	1046	1724	1343	1532	1207	488
19	Short	Inertia	0	1	1	0	0	0	0	0	0	0
20	Short	Reversal	1	0	0	2	3	2	84	2	16	5
21	Inertia	Long	4	16	40	11	8	7	2	0	8	17
22	Reversal	Long	8	1	0	0	1	0	31	5	3	3
23	Inertia	Short	2	13	105	16	13	17	1	3	6	3
24	Reversal	Short	7	1	0	1	2	2	17	69	4	1

(${\alpha }_2=2\times {10}^{-4}$), the ratio of the final balances is:

$${\displaystyle \frac{B_2}{B_1}}={\displaystyle \frac{{(1-{\alpha }_2)}^{Nk}}{{(1-{\alpha }_1)}^{Nk}}}\approx {\displaystyle \frac{e^{-{\alpha }_{2}Nk}}{e^{-{\alpha }_{1}Nk}}}=e^{-({\alpha }_2-{\alpha }_1)Nk}$$

(6)

Substituting the values for number of days $N=6750$ and $k=2$ trades per day:

$${\displaystyle \frac{B_2}{B_1}}\approx e^{-\left(0.0001\right)\left(13500\right)}=e^{-1.35}\approx 0.259$$

(7)

This confirms that regardless of the underlying strategy’s strength, a jump from 1 bp to 2 bps in transaction costs will automatically eliminate approximately $74\%$ of the final wealth due to the nature of continuous compounding.

Results and Discussion: 1 Basis Point Transaction Cost

The effect of 1 basis point transaction cost (typical for professional hedge funds) is illustrated in Table 11.

The introduction of 1 basis point (0.01%) transaction costs per trade fundamentally alters the strategy landscape, reducing profitable strategies from 42 to only 13 out of 240 combinations. This dramatic 69% reduction in profitability demonstrates the critical importance of transaction costs in momentum strategy viability, as predicted by Equation (4), where the compounding friction effect over $N=6750$ trading days yields approximately 51% wealth erosion.

Survival of overnight momentum strategies: Strategy #1 (Long, Cash) remains profitable in 9 of 10 ETFs, though the final values decline substantially from the zero-cost scenario: XLK ($856, down from $3165), XLE ($643, down from $2378), and XLI ($481, down from $1778). The persistence of profitability despite 73% value destruction confirms that overnight momentum effects are sufficiently strong to withstand realistic implementation costs in most sectors. Only XLP ($118) shows marginal profitability, reflecting the defensive sector’s weaker momentum.

Buy-and-hold remains dominant: Strategy #5 (Long, Long) maintains identical performance ($422–$1169) as it requires only one initial trade over the entire 25-year period, incurring negligible transaction costs. With 1 bp costs, buy-and-hold now outperforms Strategy #1 in 7 of 10 ETFs, reversing the zero-cost comparison. This shift demonstrates that passive strategies gain relative advantage as trading frequency increases, consistent with the ${(1-\alpha )}^{Nk}$ friction model where $k=2$ daily trades for active strategies versus $k\approx 0$ for buy-and-hold.

Collapse of high-frequency strategies: Strategy #8 (Long, Short), which previously achieved exceptional results (XLU: $7189; XLK: $3210), now generates severe losses across all ETFs ($16–$526) due to its $k=4$ daily trade requirement. The strategy’s exposure to ${(1-0.0001)}^{4\times 6750}\approx 0.26$ compounding friction eliminates 97% of theoretical wealth. Strategy #7 (Short/Long) becomes effectively worthless ($0–$2), confirming that strategies combining negative expected returns with high trading costs are economically unviable.

Mixed strategy resilience: Long/Reversal: Strategy #18 (Long, Reversal) demonstrates remarkable resilience, remaining profitable in eight ETFs despite transaction costs: XLK ($7342), XLU ($6627), XLV ($5218), XLP ($5476), XLI ($4365), XLY ($2038), and XLF ($1460). While these values represent 76–88% declines from zero-cost levels, the strategy’s combination of reliable overnight drift capture with daytime reversal exploitation generates sufficient gross returns to overcome the ${(1-\alpha )}^{2.2N}$ friction burden, where $k\approx 2.2$ trades per day for this strategy. This is discussed in detail in Section 10.

The strategy’s continued dominance over buy-and-hold in six of 10 ETFs indicates that tactical momentum positioning can generate alpha even after accounting for realistic costs. The exceptions are SPY, XLB, XLE, and XLY, where the buy-and-hold strategy’s zero-friction advantage outweighs the mixed strategy’s gross return superiority.

Dynamic strategy fragility: Pure dynamic strategies show extreme sensitivity to transaction costs. Strategy #13 (Inertia, Inertia) remains profitable only in XLE ($3610, down from $12,982), representing a 72% decline despite this sector’s exceptional momentum strength. All other ETFs show final values below $200, with most below $10. This fragility reflects these strategies’ variable trade frequency ($k\approx 2.0$, with high variance) and their dependence on capturing consecutive momentum persistence, which becomes economically unviable when friction consumes a significant fraction of individual sub-period returns.

Strategy #14 (Inertia, Reversal) maintains profitability only in XLF ($497, down from $1795), while Strategy #16 (Reversal, Reversal) succeeds only in XLP ($5336, down from $20,707). These isolated successes represent sector-specific anomalies rather than broadly applicable patterns.

Sector-specific patterns under friction: The cross-sectional distribution of profitable strategies reveals important sector characteristics:

• Technology (XLK): Retains the strongest overnight effect post-costs (Strategy #1: $856) and remains the best performer for Strategy #18 ($7342), indicating this sector’s momentum strength exceeds typical friction levels.
• Energy (XLE): Shows continued momentum viability (Strategy #1: $643; #13: $3610; #17: $5307), confirming commodity-driven momentum patterns generate sufficient returns to overcome implementation costs.
• Consumer Staples (XLP): Exhibits unique reversal strength (Strategy #10: $1388; #16: $5336), though all values decline dramatically from zero-cost levels. This defensive sector’s mean reversion tendencies are more resilient to transaction costs than momentum effects in most other sectors.
• Utilities (XLU): Maintains strong Strategy #18 performance ($6627) but shows substantial erosion in Strategy #8 (from $7189 to $526), indicating the sector’s daytime reversal patterns remain exploitable, but pure arbitrage between sub-periods becomes marginal.

Practical implications: At 1 bp per trade—representative of institutional trading costs for liquid ETFs—only strategies with either (a) low trading frequency (buy-and-hold) or (b) exceptionally strong gross returns combined with moderate frequency (Long, Cash), (Long, Reversal) remain economically viable. The 89% reduction in total profitable strategies (from 42 to 13) demonstrates that transaction costs serve as a powerful selection mechanism, filtering out marginally profitable approaches while preserving only those strategies with substantial gross return advantages.

5.2. Performance Under 2 Basis Points’ Transaction Cost

Table 12 reveals the severe impact of doubling transaction costs to 2 basis points per trade.

As predicted by Equation (7), the ratio $B_2/B_1\approx 0.259$ indicates that wealth levels at 2 bps are approximately 26% of those at 1 bp, representing an additional 74% wealth destruction regardless of underlying strategy strength.

Results and Discussion: 2 Basis Points’ Transaction Cost

Dramatic contraction of viable strategies: Only 7 strategies across all 240 combinations remain profitable at 2 bps transaction costs, representing a 46% reduction from the 13 profitable strategies at 1 bp and an 83% reduction from the 42 profitable strategies under zero costs. This nonlinear deterioration—where doubling costs from 1 bp to 2 bps eliminates 46% of the remaining profitable strategies rather than reducing them proportionally—demonstrates that many strategies operate near the break-even threshold, where modest cost increases trigger a significant decline in profitability.

Overnight momentum becomes marginal: Strategy #1 (Long, Cash) now generates losses in all 10 ETFs, with final values ranging from $32 (XLP) to $232 (XLK), representing 63–73% declines from 1 bp levels. Even XLK, which maintained $856 at 1 bp, falls to $232, confirming that pure overnight momentum strategies—despite capturing genuine market inefficiencies—cannot overcome the ${(1-0.0002)}^{2\times 6750}\approx 0.26$ compounding friction when executing approximately 13,500 trades over the study period.

This universal failure of Strategy #1 represents a critical threshold: overnight momentum effects, while statistically significant and economically meaningful under low-cost regimes, become uneconomical for most ETF sectors when per-trade costs exceed 1.5–2 basis points. The exception is XLK ($232), which remains closest to profitability, suggesting that technology sector momentum might survive costs slightly above 2 bps.

Buy-and-hold dominance: Strategy #5 (Long, Long) maintains virtually identical performance ($422–$1169) and now outperforms all active strategies in all ETFs. The strategy’s immunity to transaction costs—resulting from single-trade implementation—provides a 200–800% return advantage over the next-best alternatives. This finding has profound implications for retail investors and institutions with higher trading costs: passive buy-and-hold becomes the dominant strategy when transaction costs exceed 1.5–2 bps, even in the presence of statistically significant momentum effects.

Long/Reversal survival in select sectors: Strategy #18 (Long, Reversal) remains the only active strategy maintaining broad profitability, succeeding in five ETFs: XLK ($1724), XLU ($1532), XLP ($1343), XLV ($1207), and XLI ($1046). These final values represent 77–88% declines from 1 bp levels but still exceed the initial $100 investment by 950–1624%, demonstrating that the strategy’s combination of overnight momentum and daytime reversal generates sufficient gross returns to overcome substantial friction.

However, Strategy #18 now underperforms buy-and-hold across all 10 ETFs, indicating that even this optimal active strategy cannot justify its transaction costs relative to passive alternatives. The strategy’s continued profitability suggests it may remain viable for investors with costs below 2 bps (1.5–1.8 bps range) but becomes dominated by passive alternatives at higher cost levels.

Dynamic strategy extinction: Nearly all dynamic strategies become unprofitable:

• Strategy #13 (Inertia, Inertia): profitable only in XLE ($1004, down from $3610), representing a 72% decline and the strategy’s last remaining viable sector.
• Strategy #16 (Reversal, Reversal): maintains profitability only in XLP ($1375, down from $5336), reflecting this sector’s unique mean reversion characteristics.
• Strategy #17 (Long/Inertia): survives only in XLE ($1613, down from $5307), confirming Energy’s exceptional momentum strength.

All other dynamic strategies generate final values below $400, with most below $100. The concentration of surviving strategies in XLE and XLP—representing extreme momentum (Energy) and mean reversion (Consumer Staples) characteristics—suggests that only sectors with the strongest directional tendencies can support active strategies under realistic retail conditions trading costs (Frazzini et al. 2018; Korajczyk and Sadka 2004).

Cost threshold analysis: The empirical evidence demonstrates clear profitability thresholds:

• 0–1 bp: overnight momentum (Strategy #1) and mixed strategies (Strategy #18) are broadly profitable across 8–9 ETFs, with exceptional performers achieving 1500–3000% returns.
• 1–2 bps: overnight momentum becomes marginal; only Strategy #18 maintains broad profitability (8 ETFs), though underperforming buy-and-hold.
• Above 2 bps: only buy-and-hold and sector-specific dynamic strategies (XLE, XLP) remain viable; active momentum strategies become uneconomical.

These thresholds align with institutional trading cost estimates: large institutions trading liquid ETFs typically incur total costs of 0.5–1.5 bps (spread + commission + market impact), while retail investors face costs of 2–5 bps. The empirical results suggest that momentum strategies remain viable for institutional investors but are increasingly dominated by passive alternatives for most retail participants.

Sector differentiation under high costs: The cross-sectional pattern of surviving strategies reveals fundamental differences in exploitable inefficiencies:

• Technology (XLK): Maintains the strongest Strategy #18 performance ($1724), indicating persistent overnight-daytime asymmetries survive higher friction levels. This likely reflects the sector’s concentration of companies that frequently hold after-hours earnings events and make product announcements.
• Energy (XLE): Supports multiple profitable strategies (#13: $1004; #17: $1613), confirming commodity-driven momentum generates returns exceeding typical friction levels. The 24-h nature of global oil markets creates a continuous information flow supporting momentum persistence.
• Consumer Staples (XLP): Unique reversal profitability (Strategy #16: $1375) persists despite high costs, suggesting this defensive sector’s mean reversion tendencies represent fundamental valuation anchoring rather than noise trading.
• Healthcare (XLV) and Utilities (XLU): Strategy #18 maintains profitability ($1207 and $1532), indicating these sectors’ combination of overnight news sensitivity (regulatory announcements, clinical trial results) and intraday adjustment patterns remains exploitable.

Implications for strategy implementation: The 2 bps results provide critical guidance for practical implementation:

1. Institutional investors (0.5–1.5 bps costs) can profitably exploit overnight momentum through Strategy #1 and mixed approaches (Strategy #18), particularly in Technology, Energy, and Utilities sectors.

2. Retail investors (2–5 bps costs) should avoid active momentum strategies and default to buy-and-hold (Strategy #5), as transaction costs eliminate the alpha generation potential of tactical positioning.

3. Sector selection becomes critical: investors should concentrate active strategies in sectors with the strongest momentum effects (XLK, XLE, XLU) and avoid those with weaker patterns (XLF, XLY, XLV under 2 bps).

4. Strategy frequency matters decisively: high-frequency approaches (Strategies #7, #8 with $k=4$ trades/day) become immediately uneconomical, while moderate-frequency strategies (Strategies #1, #18 with $k=2$ trades/day) remain viable only under low-cost regimes.

The transaction cost analysis confirms that overnight momentum represents a genuine market inefficiency that can be exploited under institutional cost structures; however, the effect is largely eliminated for typical retail investors, who face higher trading costs. This finding reconciles the academic literature documenting overnight momentum effects with the practical observation that most retail investors underperform passive benchmarks: the inefficiency exists but is only accessible to low-cost traders.

5.3. Transaction Cost Sensitivity Analysis

To address concerns about the simplified fixed-cost model and to provide a fuller picture of strategy viability,

Table 13. Transaction cost sensitivity analysis—SPY. Final value ($100 initial), Sharpe ratio, and CAGR for five key strategies at cost levels 0–5 bps. Asterisk (*) denotes unprofitable (final value < $100 or negative CAGR).

Strategy	Transaction Cost (bps Per Trade)
	0	0.5	1	1.5	2	2.5	3	3.5	4	4.5	5
Final Value ($)
Long+Long (B&H)	547	547	547	547	547	547	547	547	547	546	546
Long+Cash	525	525	525	525	525	525	525	525	525	525	525
Long+Reversal	2292	1622	1148	812	575	407	288	204	144	102	72 *
Reversal+Reversal	2203	1092	542	269	133	66 *	33 *	16 *	8 *	4 *	2 *
Cash+Reversal	437	309	219	155	109	77 *	55 *	39 *	27 *	19 *	14 *
Sharpe Ratio
Long+Long (B&H)	0.32	0.32	0.32	0.32	0.32	0.32	0.32	0.32	0.32	0.32	0.32
Long+Cash	0.43	0.43	0.43	0.43	0.43	0.43	0.43	0.43	0.43	0.43	0.43
Long+Reversal	0.60	0.53	0.46	0.40	0.33	0.26	0.20	0.13	0.06	0.00 *	−0.07 *
Reversal+Reversal	0.59	0.45	0.32	0.18	0.05	−0.09 *	−0.22 *	−0.36 *	−0.50 *	−0.63 *	−0.77 *
Cash+Reversal	0.30	0.22	0.14	0.05	−0.03 *	−0.11 *	−0.19 *	−0.28 *	−0.36 *	−0.44 *	−0.52 *
CAGR (%)
Long+Long (B&H)	6.52	6.52	6.52	6.52	6.52	6.52	6.51	6.51	6.51	6.51	6.51
Long+Cash	6.36	6.35	6.35	6.35	6.35	6.35	6.35	6.35	6.35	6.35	6.35
Long+Reversal	12.34	10.91	9.49	8.09	6.71	5.35	4.00	2.68	1.36	0.07	−1.21 *
Reversal+Reversal	12.18	9.29	6.48	3.74	1.07	−1.53 *	−4.06 *	−6.53 *	−8.94 *	−11.28 *	−13.57 *
Cash+Reversal	5.63	4.28	2.95	1.63	0.34	−0.95 *	−2.21 *	−3.46 *	−4.69 *	−5.91 *	−7.11 *

presents the final portfolio value, Sharpe ratio, and CAGR for the five key strategies across the complete range from 0 to 5 bps for SPY, which is representative of the broad cross-section. The comparison of the growth of these strategies without transaction costs is shown in Figure 8. The comparison of the growth of these strategies with 1 bps transaction cost is shown in Figure 9. Finally, the comparison of the growth of these strategies with 2 bps transaction cost is shown in Figure 10.

The sensitivity analysis reveals clear, monotonic degradation. Strategy #18 (Long+Reversal) remains the strongest active strategy at every cost level up to 4.5 bps, generating a positive CAGR of 0.07% at 4.5 bps before turning negative at 5 bps. Buy-and-hold is effectively cost-free (CAGR 6.51–6.52% across the full range), confirming its dominance for high-cost investors. The results also address the concern about wider spreads at the open and close: even if the true all-in cost at these times were 50% higher than our baseline assumption (e.g., 1.5 bps instead of 1 bps for an institutional investor), Strategy #18 would still deliver a Sharpe ratio of 0.40 and CAGR of 8.09%, remaining clearly profitable. The overnight long strategy (Long+Cash) is fully immune to cost escalation beyond 0.5 bps because its overnight return advantage is sufficiently large and consistent—its Sharpe ratio stays at 0.43 across the entire 0–5 bps range—making it a robust choice even under conservative cost assumptions.

• Section summary: The growth analysis establishes three findings. First, temporal decomposition into overnight and daytime sub-periods generates substantial alpha: Strategy #18 (Long, Reversal) and Strategy #1 (Long, Cash) dominate across most ETFs at zero cost. Second, transaction costs are the binding constraint: viable strategies fall from 42 to 13 to 7 as costs rise from 0 to 1 to 2 bps. Third, the TC sensitivity analysis (Table 13) shows Strategy #18 remains profitable up to 4.5 bps with a monotone but gradual decline, confirming robustness to moderate cost uncertainty including wider open/close spreads.

6. Risk-Adjusted Performance Analysis

6.1. Sharpe Ratio Evaluation

While absolute returns provide initial insight into a strategy’s profitability, risk-adjusted performance metrics are essential for evaluating whether it generates returns commensurate with its level of volatility exposure. The Sharpe ratio, defined as the ratio of excess returns to standard deviation, offers a standardized measure for comparing strategies with different risk profiles (Sharpe 1966).

Table 14. Average yearly Sharpe ratio by strategy and ETF. Blue color in Strategy #5 indicates the Sharpe ratio for the passive Buy&Hold (long, long) strategy. The green color indicates that the corresponding strategy has a higher Sharpe ratio than the passive strategy. Finally, red color indicates that the corresponding strategy has a lower Sharpe ratio than the passive strategy.

#	Strategy		SPY	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY
	Overnight	Daytime
1	Long	Cash	1.01	0.88	1.02	0.95	1.01	1.07	0.50	1.32	0.96	0.78
2	Short	Cash	−1.51	−1.27	−1.35	−1.29	−1.41	−1.41	−1.08	−1.89	−1.44	−1.16
3	Cash	Long	0.11	−0.01	−0.16	−0.06	−0.00	−0.00	0.16	−0.22	−0.05	0.18
4	Cash	Short	−0.44	−0.23	−0.04	−0.19	−0.27	−0.24	−0.52	−0.05	−0.25	−0.45
5	Long	Long	0.73	0.51	0.46	0.56	0.65	0.72	0.56	0.58	0.59	0.70
6	Short	Short	−1.00	−0.72	−0.62	−0.78	−0.90	−0.95	−0.90	−0.85	−0.89	−0.94
7	Short	Long	−0.62	−0.57	−0.73	−0.65	−0.66	−0.70	−0.22	−0.83	−0.58	−0.38
8	Long	Short	0.34	0.36	0.55	0.46	0.45	0.52	−0.05	0.61	0.35	0.18
9	Cash	Inertia	−0.22	0.11	0.29	−0.56	−0.84	−0.67	−1.35	−0.87	−0.97	−0.63
10	Cash	Reversal	−0.11	−0.35	−0.50	0.32	0.56	0.42	0.99	0.59	0.67	0.37
11	Inertia	Cash	−0.79	0.14	0.67	0.11	0.11	−0.04	−0.97	−0.88	−0.26	−0.14
12	Reversal	Cash	0.30	−0.52	−1.00	−0.45	−0.50	−0.30	0.39	0.33	−0.21	−0.24
13	Inertia	Inertia	−0.44	0.27	0.71	−0.32	−0.58	−0.48	−1.45	−1.03	−0.81	−0.47
14	Inertia	Reversal	−0.30	−0.11	0.05	0.42	0.61	0.44	0.45	0.24	0.53	0.35
15	Reversal	Inertia	0.03	−0.10	−0.22	−0.60	−0.83	−0.62	−0.76	−0.49	−0.78	−0.57
16	Reversal	Reversal	0.16	−0.47	−0.90	0.10	0.33	0.25	1.14	0.78	0.54	0.25
17	Long	Inertia	0.47	0.63	0.83	0.16	−0.02	0.17	−0.69	−0.00	−0.17	0.03
18	Long	Reversal	0.61	0.25	0.17	0.88	1.16	1.09	1.23	1.25	1.19	0.87
19	Short	Inertia	−0.89	−0.47	−0.35	−1.09	−1.40	−1.31	−1.54	−1.50	−1.47	−1.10
20	Short	Reversal	−0.73	−0.82	−1.01	−0.35	−0.20	−0.36	0.39	−0.24	−0.08	−0.24
21	Inertia	Long	−0.16	0.16	0.34	0.10	0.16	0.08	−0.23	−0.46	−0.04	0.20
22	Reversal	Long	0.29	−0.21	−0.60	−0.22	−0.19	−0.10	0.49	0.11	−0.04	0.08
23	Inertia	Short	−0.56	0.01	0.43	0.03	−0.03	−0.10	−0.79	−0.35	−0.23	−0.31
24	Reversal	Short	−0.11	−0.36	−0.52	−0.30	−0.39	−0.28	−0.08	0.21	−0.21	−0.41

presents the average yearly Sharpe ratios for all 24 strategies across the ten sector ETFs over the 1999–2024 period.

The Sharpe ratio is calculated as follows:

$$\mathrm{Sharpe}\mathrm{Ratio}={\displaystyle \frac{\overline{R}-R_f}{{\sigma }_R}}$$

(8)

where $\overline{R}$ is the average annual return, $R_f$ is the risk-free rate (assumed to be zero for comparative purposes), and ${\sigma }_R$ is the standard deviation of annual returns. Positive Sharpe ratios indicate strategies that generate positive risk-adjusted returns; values above 0.5 are generally considered acceptable, above 1.0 good, and above 2.0 excellent by industry standards.

6.2. Results and Discussion

6.2.1. Superior Risk-Adjusted Performance of Overnight Strategies

Strategy #1 (Long/Cash) demonstrates consistently strong risk-adjusted returns with Sharpe ratios ranging from 0.50 (XLP) to 1.32 (XLU), with 9 of 10 ETFs exceeding 0.78. The strategy achieves Sharpe ratios above 1.0 in five sectors (XLU: 1.32, XLK: 1.07, XLE: 1.02, XLI: 1.01, SPY: 1.01), indicating that overnight momentum generates not only positive absolute returns but also favorable risk-adjusted returns exceeding those of many traditional investment strategies. The exceptional performance in Utilities (1.32) reflects this sector’s combination of strong overnight drift with relatively low overnight volatility.

In stark contrast, Strategy #2 (Short, Cash) exhibits uniformly negative Sharpe ratios ranging from $-1.08$ to $-1.89$, with particularly severe risk-adjusted losses in XLU ($-1.89$), XLV ($-1.44$), and XLI ($-1.41$). These deeply negative values confirm that shorting overnight momentum not only generates losses but does so with high volatility, creating compounded risk-adjusted underperformance. The symmetry in magnitude but opposition in sign between Strategies #1 and #2 validates that overnight drift represents a persistent directional anomaly rather than a volatility artifact.

6.2.2. Weak Risk-Adjusted Returns from Daytime Strategies

Pure daytime strategies show minimal risk-adjusted performance. Strategy #3 (Cash/Long) generates Sharpe ratios near zero across most ETFs, ranging from $-0.22$ (XLU) to 0.18 (XLY), with 8 of 10 ETFs showing absolute values below 0.20. This near-zero performance suggests that daytime momentum is either absent or insufficiently strong to offset the volatility incurred during regular trading hours. The exceptions—XLP (0.16) and XLY (0.18)—show modest positive risk-adjusted returns but remain far below overnight strategy performance.

Strategy #4 (Cash, Short) exhibits consistently negative Sharpe ratios across all sectors ($-0.52$ to $-0.04$), confirming that shorting during the day generates risk-adjusted losses, though less severe than shorting overnight. The relatively better performance (less negative) of daytime shorting compared to overnight shorting suggests that while daytime periods lack strong momentum effects, they also lack the persistent positive drift that characterizes overnight periods.

6.2.3. Buy-and-Hold Risk-Adjusted Performance

Strategy #5 (Long, Long) delivers solid risk-adjusted returns, with Sharpe ratios ranging from 0.46 (XLE) to 0.73 (SPY), and all ten ETFs showing positive Sharpe ratios between 0.46 and 0.73. The consistency of these moderate Sharpe ratios reflects the fundamental risk–return characteristics of equity investments over extended periods. Notably, buy-and-hold underperforms Strategy #1 on a risk-adjusted basis in 9 of 10 ETFs, indicating that overnight momentum capture improves Sharpe ratios by 7–81% compared to passive holding (e.g., XLU: 1.32 vs. 0.58 represents 128% improvement).

The single exception is XLY (0.70 for buy-and-hold vs. 0.78 for overnight), where the long-term secular growth in consumer discretionary spending during the 1999–2024 period generated risk-adjusted returns competitive with those of overnight momentum strategies. This finding suggests that in strongly trending sectors, buy-and-hold can achieve risk-adjusted performance comparable to that of active momentum strategies, although it still underperforms in absolute return terms.

6.2.4. Mixed Strategy Excellence: Long/Reversal

Strategy #18 (Long, Reversal) achieves the highest risk-adjusted returns across the broadest set of ETFs, with Sharpe ratios ranging from 0.17 (XLE) to 1.25 (XLU). The strategy exceeds 1.0 in four sectors: XLU (1.25), XLP (1.23), XLV (1.19), and XLI (1.16), representing exceptional risk-adjusted performance that places it in the top decile of documented investment strategies in academic literature. The strategy also shows strong performance in XLK (1.09), XLF (0.88), and XLY (0.87).

The superior Sharpe ratios of Strategy #18 compared to Strategy #1 in most sectors (7 of 10 ETFs) demonstrate that combining overnight momentum with daytime mean reversion improves risk-adjusted returns beyond pure overnight exposure. This enhancement occurs through two mechanisms: (1) capturing additional returns from daytime reversals, and (2) potentially reducing portfolio volatility through the offsetting nature of overnight momentum and daytime reversal positioning. The strategy’s broad success across diverse sectors—defensive (XLP, XLU), cyclical (XLI, and healthcare (XLV)—indicates robustness across different fundamental and risk characteristics.

The exceptions where Strategy #18 underperforms Strategy #1 on a risk-adjusted basis are XLE (0.17 vs. 1.02), XLB (0.25 vs. 0.88), and SPY (0.61 vs. 1.01). For Energy, the underperformance likely reflects the sector’s strong intraday momentum continuation following overnight gaps, where the strategy’s contrarian daytime positioning counters persistent commodity-driven trends. For Materials (XLB), similar commodity linkages may create momentum persistence that makes reversal positioning suboptimal.

6.2.5. Dynamic Strategy Performance

Pure dynamic strategies exhibit highly variable, generally poor risk-adjusted performance. Strategy #13 (Inertia/Inertia) demonstrates extreme sector dependence: strong positive Sharpe ratios in XLE (0.71) and XLB (0.27), but deeply negative values in most other sectors, including XLP ($-1.45$), XLU ($-1.03$), XLV ($-0.81$), and XLI ($-0.58$). This pattern confirms that double-momentum strategies work only in sectors with exceptional trending characteristics (commodity-linked sectors), generating severe risk-adjusted losses elsewhere.

Strategy #14 (Inertia/Reversal) shows more consistent positive risk-adjusted performance across multiple sectors, with Sharpe ratios ranging from $-0.30$ (SPY) to 0.61 (XLI). The strategy achieves respectable Sharpe ratios in XLI (0.61), XLV (0.53), XLP (0.45), and XLK (0.44), indicating that combining overnight momentum with daytime reversal signals can generate positive risk-adjusted returns even without the static overnight long position of Strategy #18. However, the strategy underperforms Strategy #18 in all sectors, suggesting that the static overnight long position provides superior risk-adjusted returns compared to conditional overnight positioning based on prior daytime movements.

Reversal strategies (Strategy #16: Reversal/Reversal) show exceptional sector-specific performance in XLP (1.14) and XLU (0.78) but fail in most other sectors with negative or near-zero Sharpe ratios. This concentration suggests that mean-reversion strategies are highly sector-dependent and work primarily in defensive, stable sectors with strong valuation anchoring, rather than in cyclical or growth-oriented sectors.

6.2.6. Sector-Specific Risk–Return Characteristics

Cross-sectional analysis reveals fundamental differences in sector risk–return profiles:

• Utilities (XLU): Exhibits the strongest risk-adjusted overnight momentum (Strategy #1: 1.32) and mixed strategy performance (Strategy #18: 1.25), reflecting this sector’s unique combination of strong overnight sensitivity to interest rate changes and regulatory news with relatively low volatility. The sector’s bond-like characteristics create predictable overnight gaps without excessive noise.
• Technology (XLK): Shows consistently strong Sharpe ratios for overnight strategies (Strategy #1: 1.07; #18: 1.09), confirming that the sector’s after-hours earnings announcements and product news create persistent overnight momentum with acceptable volatility. The near-identical Sharpe ratios between pure overnight and mixed strategies suggest that daytime reversals in technology stocks are relatively minor.
• Energy (XLE): Demonstrates the highest dynamic momentum Sharpe ratio (Strategy #13: 0.71; #17: 0.83), reflecting commodity price persistence across multiple sub-periods. However, the sector shows lower Sharpe ratios for reversal-based strategies, indicating that mean reversion is weak in commodity-driven markets.
• Consumer Staples (XLP): Exhibits unique reversal characteristics with the highest Sharpe ratio for Strategy #16 (1.14) and strong Strategy #18 performance (1.23). This defensive sector’s mean reversion tendencies, combined with moderate overnight momentum, create favorable conditions for mixed strategies that exploit both patterns.
• Healthcare (XLV): Shows balanced performance across momentum strategies with Strategy #18 achieving a 1.19 Sharpe ratio, reflecting the sector’s combination of overnight clinical trial results and regulatory announcements with relatively stable intraday trading patterns.

6.2.7. Negative Sharpe Ratio Patterns

Short strategies universally exhibit deeply negative Sharpe ratios, with Strategy #19 (Short, Inertia) showing the most severe risk-adjusted losses across all sectors ($-0.35$ to $-1.54$). These extremely negative values (often below $-1.0$) indicate that short momentum strategies not only lose money but also do so with high volatility, resulting in compounded wealth destruction on a risk-adjusted basis. The consistency of this pattern across all sectors and strategy variations confirms that equity markets exhibit persistent positive drift that cannot be profitably shorted using systematic momentum or reversal approaches.

Strategy #15 (Reversal, Inertia) similarly shows uniformly negative Sharpe ratios ($-0.10$ to $-0.83$), demonstrating that attempting to fade overnight momentum while following daytime momentum creates unfavorable risk–return tradeoffs. This combination counters the strongest market pattern (overnight drift) while attempting to capitalize on the weaker pattern (daytime momentum), resulting in consistent, risk-adjusted losses.

6.2.8. Comparison with Traditional Benchmarks

The Sharpe ratios reported for optimal strategies in this study compare favorably with those of traditional investment approaches. Historical S&P 500 Sharpe ratios over comparable periods typically range from 0.40 to 0.60, while actively managed mutual funds average 0.30 to 0.50 after fees. Our Strategy #18 achieves Sharpe ratios exceeding 1.0 in four sectors and above 0.85 in seven sectors, placing these approaches in the top performance quartile of documented investment strategies.

However, these Sharpe ratios reflect theoretical performance, not transaction costs. As demonstrated in the previous section, transaction costs above 1–2 bps substantially reduce absolute returns, which proportionally reduces Sharpe ratios since volatility remains unchanged. For investors facing 2+ basis points (bps) costs, the risk-adjusted performance of active momentum strategies deteriorates to levels comparable with or below buy-and-hold benchmarks, reinforcing the conclusion that these strategies remain viable only for low-cost institutional traders.

6.2.9. Implications for Portfolio Construction

The Sharpe ratio analysis provides several insights for portfolio construction:

1.

Overnight momentum strategies (Strategy #1) offer superior risk-adjusted returns to buy-and-hold in most sectors, suggesting that tactical overnight positioning can improve portfolio efficiency for low-cost traders.

2.

Mixed strategies (Strategy #18) achieve the best risk-adjusted performance across diverse sectors, indicating that combining multiple temporal momentum patterns creates more efficient portfolios than exploiting single patterns.

3.

Sector allocation matters significantly: concentrating active strategies in sectors with the highest Sharpe ratios (XLU, XLK, XLV, XLP for Strategy #18) can substantially improve overall portfolio risk-adjusted returns compared to equal-weight or market-cap-weight approaches.

4.

Short strategies should be avoided entirely, as they generate deeply negative risk-adjusted returns across all sectors and strategy variations, indicating that equity market drift is too persistent to profit from systematic shorting approaches.

The risk-adjusted performance analysis confirms that overnight momentum represents not merely a source of absolute returns but also an improvement in portfolio efficiency, generating superior Sharpe ratios compared to traditional buy-and-hold strategies across most ETF sectors studied. However, this efficiency advantage remains contingent on maintaining low transaction costs below the 2–3 bps threshold identified in the Section 5.3.

• Section summary: Risk-adjusted analysis confirms that Strategy #1 (Sharpe $\approx 0.95$ averaged across ETFs) and Strategy #18 (Sortino $\approx 1.58$) dominate all alternatives on a risk-adjusted basis. Both exceed buy-and-hold’s Sharpe of 0.61 by 56% and 43%, respectively. Short strategies are universally negative. Sector differences are meaningful: XLU and XLK show the strongest Sharpe ratios for Strategy #18, while XLE favors the pure overnight strategy.

7. Volatility Analysis Across All Strategies

7.1. Strategy Volatility Profiles

Understanding the volatility characteristics of trading strategies is crucial for evaluating their risk profiles and determining their suitability for various investor risk tolerances. Volatility, measured as the annualized standard deviation of returns, directly affects the denominator of the Sharpe ratio and reflects the uncertainty investors face in strategy outcomes.

Table 15. Average yearly volatility (%) by strategy and ETF. Blue color in Strategy #5 indicates the volatility for the passive Buy&Hold (long, long) strategy. The green color indicates that the corresponding strategy has lower volatility than the passive strategy. Finally, red color indicates that the corresponding strategy has higher volatility than the passive strategy.

#	Strategy		SPY	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY
	Overnight	Daytime
1	Long	Cash	9.9	12.3	14.5	15.0	11.8	14.3	8.4	8.8	9.8	12.7
2	Short	Cash	9.9	12.3	14.5	15.0	11.8	14.3	8.4	8.8	9.8	12.7
3	Cash	Long	14.3	18.4	21.5	20.0	16.2	19.4	12.6	16.3	14.7	17.5
4	Cash	Short	14.3	18.4	21.5	20.0	16.2	19.4	12.6	16.3	14.7	17.5
5	Long	Long	17.6	22.2	26.4	24.6	19.6	23.5	14.2	17.9	16.8	20.9
6	Short	Short	17.6	22.1	26.4	24.6	19.6	23.4	14.2	17.9	16.8	20.9
7	Short	Long	17.4	22.4	25.7	25.7	20.6	24.9	16.1	19.2	18.5	22.4
8	Long	Short	17.4	22.3	25.7	25.6	20.6	24.8	16.1	19.2	18.5	22.4
9	Cash	Inertia	14.3	18.4	21.5	20.0	16.1	19.4	12.5	16.2	14.6	17.5
10	Cash	Reversal	14.3	18.4	21.5	20.0	16.1	19.4	12.5	16.2	14.6	17.5
11	Inertia	Cash	10.0	12.3	14.5	15.0	11.9	14.4	8.4	8.9	9.9	12.7
12	Reversal	Cash	10.0	12.3	14.5	15.0	11.9	14.4	8.4	8.9	9.9	12.7
13	Inertia	Inertia	17.3	22.2	25.8	24.1	19.5	23.3	15.2	18.4	17.5	21.5
14	Inertia	Reversal	17.8	22.3	26.3	26.2	20.6	25.1	15.1	18.8	17.8	21.9
15	Reversal	Inertia	17.8	22.3	26.3	26.0	20.5	25.0	15.1	18.8	17.8	21.9
16	Reversal	Reversal	17.3	22.2	25.7	24.1	19.5	23.3	15.2	18.4	17.5	21.5
17	Long	Inertia	17.9	22.6	26.1	25.4	20.2	24.6	15.3	18.6	18.0	21.8
18	Long	Reversal	17.1	21.8	26.0	24.8	19.8	23.7	15.0	18.5	17.2	21.5
19	Short	Inertia	17.1	21.8	26.0	24.7	19.8	23.7	15.0	18.4	17.2	21.4
20	Short	Reversal	17.9	22.7	26.1	25.5	20.3	24.7	15.3	18.7	18.0	21.9
21	Inertia	Long	17.5	22.2	25.8	24.9	20.0	24.3	15.2	18.6	18.0	22.0
22	Reversal	Long	17.5	22.3	26.4	25.4	20.4	24.3	15.3	18.8	17.5	21.4
23	Inertia	Short	17.5	22.3	26.4	25.4	20.4	24.2	15.2	18.8	17.5	21.4
24	Reversal	Short	17.5	22.1	25.7	24.8	19.9	24.1	15.2	18.5	17.9	22.0

presents the average yearly volatility (in percentage terms) for all 24 strategies across the ten sector ETFs over the 1999–2024 period.

Volatility patterns reveal important characteristics of strategy risk exposure: strategies that trade only during specific sub-periods exhibit lower volatility than those active throughout the full 24-h cycle, while strategies that switch positions frequently (short/long combinations) often show elevated volatility due to exposure to gap risk and directional changes.

7.2. Results and Discussion

7.2.1. Overnight vs. Daytime Volatility Differential

A fundamental finding emerges from comparing single-subperiod strategies: overnight periods (Strategies #1, #2) exhibit substantially lower volatility than daytime periods (Strategies #3, #4) across all 10 ETFs. Overnight volatility ranges from 8.4% (XLP) to 15.0% (XLF), while daytime volatility spans 12.5% (XLP) to 21.5% (XLE), representing a 44–48% volatility increase during regular trading hours.

This volatility differential reflects the fundamental nature of price formation in the two sub-periods. Overnight periods compress approximately 16 h of information flow into a single gap at market open, creating a more discrete price adjustment with lower measured volatility. In contrast, the 6.5-h daytime trading session involves continuous price discovery, with numerous intraday fluctuations, generating higher realized volatility even when the total price change may be relatively small Andersen (1996).

The consistency of this pattern across all sectors—defensive (XLP, XLU), cyclical (XLI, XLY), commodity (XLE), and growth (XLK)—indicates that the overnight-daytime volatility differential represents a universal market microstructure characteristic rather than sector-specific behavior. Consumer Staples (XLP) shows the lowest volatility in both sub-periods (8.4% overnight, 12.6% daytime), reflecting this defensive sector’s stable fundamental characteristics, while Energy (XLE) and Financials (XLF) exhibit the highest volatility in both sub-periods, consistent with their sensitivity to commodity prices and leverage effects, respectively.

7.2.2. Position Direction and Volatility Symmetry

Strategies #1 and #2 (Long, Cash) vs. (Short, Cash) exhibit identical volatility despite opposite position directions, as do Strategies #3 and #4 (Cash, Long) vs. (Cash, Short). This symmetry confirms that volatility measures the magnitude of price movements regardless of direction, with long and short positions facing equivalent uncertainty about outcomes. The identical volatilities validate that our volatility calculations capture true price variation rather than directional return effects.

Similarly, Strategies #11 and #12 (Inertia, Cash) vs. (Reversal, Cash) show identical overnight volatilities (ranging from 8.4% to 15.0% across sectors), as do Strategies #9 and #10 for daytime volatility. This indicates that dynamic positioning based on prior sub-period momentum does not materially alter the volatility exposure—the uncertainty about price movements remains the same whether positions align with or against prior momentum.

7.2.3. Full-Cycle Strategy Volatility

Strategies active throughout both sub-periods (Strategies #5–#8, #13–#24) exhibit substantially higher volatility than single sub-period strategies, ranging from 14.2% (XLP, buy-and-hold) to 26.4% (XLE, various combined strategies). Buy-and-hold (Strategy #5: Long/Long) shows volatility ranging from 14.2% to 26.4% across sectors, reflecting the standard market risk faced by passive equity investors over the 1999–2024 period.

The volatility additivity relationship approximately follows: ${\left({\sigma }^{CC}\right)}^2\approx {\left({\sigma }^{CO}\right)}^2+{\left({\sigma }^{OC}\right)}^2+2\rho \left({\sigma }^{CO}\right)\left({\sigma }^{OC}\right)$, where $\rho$ represents the correlation between overnight and daytime returns. For SPY, overnight volatility of 9.9% and daytime volatility of 14.3% combine to produce buy-and-hold volatility of 17.6%, implying a slightly negative correlation ($\rho \approx -0.15$) between overnight and daytime returns. This negative correlation is consistent with daytime periods partially reversing overnight gaps, creating a mild diversification effect.

Strategies that switch positions between sub-periods (Strategies #7, #8) show comparable or slightly elevated volatility (16.1–25.7% across sectors) compared to buy-and-hold, despite their tactical nature. Strategy #8 (Long, Short) exhibits nearly identical volatility to buy-and-hold in most sectors, indicating that being long overnight and short during the day creates similar total risk exposure to remaining continuously long, though with very different return profiles, as documented in previous sections.

7.2.4. Dynamic Strategy Volatility Patterns

Dynamic strategies employing momentum or reversal signals (Strategies #13–#16) show volatilities generally comparable to buy-and-hold, ranging from 15.1% to 26.3% across sectors. Strategy #13 (Inertia/Inertia) exhibits volatilities from 15.2% (XLP) to 25.8% (XLE), slightly below buy-and-hold in most sectors. This modest volatility reduction suggests that momentum-following positioning may provide only a minor risk reduction relative to static long exposure, though the effect is economically small (typically 1–2 percentage points).

Strategy #14 (Inertia, Reversal) and Strategy #15 (Reversal, Inertia) show slightly elevated volatilities compared to pure momentum approaches, ranging from 15.1% to 26.3%. The higher volatility likely reflects the position switching inherent in these strategies—betting on momentum in one sub-period while betting against it in the other creates exposure to bidirectional volatility rather than consistent directional exposure.

Strategy #16 (Reversal, Reversal), which bets against momentum in both sub-periods, exhibits volatilities (15.2–25.7%) nearly identical to buy-and-hold, confirming that contrarian positioning does not materially alter risk exposure. The combination of systematic reversal positions faces similar price uncertainty as maintaining consistent long exposure, with the key difference being expected return rather than volatility.

7.2.5. Mixed Strategy Volatility Efficiency

Strategies combining static overnight positioning with dynamic daytime signals (Strategies #17–#20) show volatilities ranging from 15.0% to 26.1%. Strategy #18 (Long, Reversal), which achieved the highest Sharpe ratios in the previous section, exhibits volatilities from 15.0% (XLP) to 26.0% (XLE), comparable to or slightly below buy-and-hold levels in most sectors.

The volatility comparison between Strategy #18 and Strategy #5 (buy-and-hold) reveals that mixed strategies achieve their superior Sharpe ratios primarily through higher returns rather than volatility reduction. In SPY, Strategy #18 shows 17.1% volatility versus 17.6% for buy-and-hold—a modest 2.8% reduction. The superior Sharpe ratio (1.61 vs. 0.73, as shown in Table 14) therefore stems predominantly from the strategy’s ability to generate higher returns by exploiting overnight momentum and daytime reversals, rather than providing significant volatility reduction.

However, in certain sectors, Strategy #18 achieves meaningful volatility reduction compared to buy-and-hold: XLP (15.0% vs. 14.2%, a minimal increase) and XLV (17.2% vs. 16.8%). The lower volatility of these sectors for the mixed strategy suggests that the combination of overnight long positioning with daytime reversal creates a more stable return stream than continuous long exposure, likely through the diversification effect of offsetting overnight and daytime price movements.

7.2.6. Sector Volatility Characteristics

Cross-sectional volatility patterns reveal fundamental differences in sector risk characteristics:

• Consumer Staples (XLP): Exhibits the lowest volatility across all strategies (8.4–16.1%), reflecting this defensive sector’s stable cash flows, inelastic demand, and reduced sensitivity to economic cycles. The sector’s low volatility makes it attractive to risk-averse investors, which explains why absolute returns appear modest compared to those of more volatile sectors.
• Utilities (XLU): Shows the second-lowest volatility (8.8–19.2%), consistent with this sector’s regulated business models, predictable cash flows, and bond-like characteristics. The low overnight volatility (8.8%) particularly stands out, suggesting that overnight news on interest rates and regulatory changes leads to relatively stable price adjustments.
• Energy (XLE): Demonstrates the highest volatility across most strategies (14.5–26.4%), reflecting this sector’s exposure to volatile commodity prices, geopolitical risk, and operational leverage. The high volatility explains why Energy strategies require particularly strong gross returns to achieve acceptable Sharpe ratios, as the volatility denominator penalizes risk-adjusted performance.
• Financials (XLF): Exhibits elevated volatility (15.0–26.2%), especially during overnight periods (15.0%, highest among all sectors), consistent with this sector’s leverage effects, regulatory sensitivity, and exposure to credit and interest rate risk. The 1999–2024 period encompasses the 2008 financial crisis, which substantially increased financial sector volatility.
• Technology (XLK): Shows high volatility (14.3–25.1%), reflecting the sector’s growth characteristics, earnings’ surprise potential, and rapid competitive dynamics. The elevated daytime volatility (19.4%) suggests that intraday price discovery and trading activity in technology stocks create substantial return variation during regular hours.
• Healthcare (XLV): Demonstrates moderate volatility (9.8–18.0%), balancing defensive characteristics from steady pharmaceutical demand with growth characteristics from biotech innovation. The sector’s relatively low overnight volatility (9.8%) suggests that after-hours news (clinical trials, FDA approvals) creates more predictable gap sizes than in more volatile sectors.

7.2.7. Volatility and Strategy Selection

The volatility analysis provides several insights for strategy selection and portfolio construction:

1. Lower-volatility strategies (overnight-only positioning: Strategies #1, #2, #11, #12) may appeal to risk-averse investors seeking momentum exposure with reduced volatility compared to buy-and-hold. However, single-sub-period strategies achieve lower volatility primarily by reducing market exposure (holding cash for half the day), rather than by genuine risk reduction.

2. Comparable volatility between active and passive strategies indicates that tactical momentum approaches do not inherently increase risk compared to buy-and-hold. Strategy #18’s volatility levels are comparable to buy-and-hold, suggesting that investors switching to this mixed approach would not face materially higher risk while potentially benefiting from superior returns documented in earlier sections.

3. Sector volatility differences suggest that risk-averse investors should concentrate momentum strategies in lower-volatility sectors (XLP, XLU, XLV) where absolute return levels may be lower but risk-adjusted returns (Sharpe ratios) remain attractive. Conversely, risk-tolerant investors seeking maximum absolute returns should focus on higher-volatility sectors (XLE, XLK, XLF), where momentum effects generate larger absolute gains despite elevated risk.

4. Volatility stability across strategy types (dynamic vs. static) confirms that the choice between momentum, reversal, or mixed approaches should be based primarily on expected returns and Sharpe ratios rather than volatility considerations, as risk exposure remains relatively consistent across strategy variations.

7.2.8. Volatility-Adjusted Performance Perspective

Combining the volatility results with the absolute return findings from earlier sections reveals that successful strategies achieve their performance through return generation rather than volatility reduction. Strategy #1 (Long/Cash) generates superior Sharpe ratios despite having lower volatility, primarily because it avoids daytime exposure entirely rather than through sophisticated risk management. Strategy #18 (Long, Reversal) achieves excellent Sharpe ratios with volatility comparable to buy-and-hold by generating substantially higher returns, not through volatility reduction.

This finding has important implications: momentum strategies in ETF markets do not provide “free lunches” through volatility reduction; rather, they offer improved risk-adjusted returns by exploiting persistent price patterns (overnight drift, daytime reversals) that generate excess returns for a given level of risk. Investors implementing these strategies should expect volatility levels comparable to those of traditional equity exposure and should size their positions accordingly, based on their risk tolerance, rather than expecting volatility benefits.

The volatility analysis confirms that overnight periods exhibit substantially lower volatility than daytime periods across all sectors, that full-cycle strategies experience volatility comparable to that of buy-and-hold strategies, and that successful momentum strategies achieve superior risk-adjusted performance primarily through return generation rather than risk reduction. These patterns remain consistent across the diverse market conditions of the 1999–2024 period, including the dot-com crash, financial crisis, and pandemic-induced volatility, suggesting that the volatility characteristics represent stable features of ETF price behavior rather than regime-dependent phenomena.

• Section summary: Overnight volatility is structurally lower than daytime volatility across all ten ETFs (8–15% vs. 13–22% annualised), a universal microstructure characteristic independent of sector. Full-cycle strategies face volatility comparable to buy-and-hold (≈20%), confirming that strategy choice does not materially change risk exposure. Superior Sharpe ratios for Strategies #1 and #18 arise from higher returns, not volatility reduction.

8. Maximum Drawdown Analysis Across All Strategies

8.1. Results and Discussion

Maximum drawdowns for all strategies are shown in

Table 16. Average yearly maximum drawdown (%) by strategy and ETF. Blue color in Strategy #5 indicates the maximum drawdown for the passive Buy&Hold (long, long) strategy. The green color indicates that the corresponding strategy has a lower drawdown than the passive strategy. Finally, red color indicates that the corresponding strategy has a higher drawdown than the passive strategy.

#	Strategy		SPY	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY
	Overnight	Daytime
1	Long	Cash	−8.7	−10.9	−11.4	−12.5	−10.6	−12.1	−8.4	−7.7	−9.6	−11.8
2	Short	Cash	−14.5	−17.3	−19.6	−19.6	−17.9	−20.6	−12.8	−17.5	−15.9	−18.0
3	Cash	Long	−13.9	−18.9	−22.1	−20.0	−17.2	−20.0	−13.5	−17.6	−16.3	−17.4
4	Cash	Short	−14.5	−18.1	−20.5	−19.2	−16.8	−19.3	−15.4	−15.8	−15.2	−19.0
5	Long	Long	−15.3	−20.2	−22.4	−20.9	−17.7	−20.7	−12.4	−15.8	−14.6	−18.4
6	Short	Short	−20.8	−24.4	−28.5	−25.8	−23.4	−27.5	−17.5	−22.3	−19.1	−24.9
7	Short	Long	−20.8	−25.9	−30.1	−29.4	−26.0	−29.5	−19.6	−26.8	−23.8	−26.0
8	Long	Short	−16.0	−19.7	−21.1	−22.0	−19.5	−21.8	−18.3	−17.7	−18.5	−22.0
9	Cash	Inertia	−14.6	−17.3	−19.6	−24.6	−22.3	−24.0	−20.4	−22.5	−21.7	−22.9
10	Cash	Reversal	−14.5	−21.5	−25.4	−18.7	−17.1	−17.3	−10.7	−17.7	−12.9	−17.1
11	Inertia	Cash	−11.8	−11.6	−11.6	−13.1	−11.2	−14.1	−12.1	−12.8	−10.8	−12.4
12	Reversal	Cash	−10.6	−16.4	−21.3	−17.6	−14.8	−17.0	−7.7	−8.4	−11.0	−14.8
13	Inertia	Inertia	−17.9	−19.7	−19.9	−24.6	−23.9	−24.5	−24.4	−26.1	−24.1	−24.1
14	Inertia	Reversal	−19.7	−22.7	−25.7	−22.6	−20.1	−22.3	−14.4	−21.8	−15.8	−20.8
15	Reversal	Inertia	−19.1	−23.1	−27.9	−31.3	−27.7	−30.8	−21.1	−23.7	−24.1	−27.4
16	Reversal	Reversal	−16.7	−26.8	−33.6	−22.3	−21.0	−21.0	−11.2	−17.7	−16.0	−20.3
17	Long	Inertia	−15.6	−19.2	−20.3	−24.6	−22.6	−23.8	−20.4	−20.1	−21.4	−23.4
18	Long	Reversal	−15.6	−21.7	−25.4	−20.1	−18.0	−19.2	−11.6	−16.7	−14.5	−19.0
19	Short	Inertia	−21.1	−24.2	−26.5	−31.5	−29.2	−33.4	−24.7	−28.5	−28.0	−29.3
20	Short	Reversal	−21.0	−28.4	−33.2	−25.4	−23.1	−25.9	−14.2	−23.7	−19.1	−22.8
21	Inertia	Long	−19.0	−20.9	−22.4	−23.8	−19.7	−23.2	−17.5	−22.6	−18.8	−20.7
22	Reversal	Long	−16.8	−24.4	−29.5	−24.8	−22.3	−26.8	−14.7	−18.6	−19.1	−22.0
23	Inertia	Short	−19.0	−20.6	−20.8	−21.6	−19.2	−23.7	−20.1	−21.1	−17.8	−22.6
24	Reversal	Short	−17.8	−24.7	−29.4	−26.0	−22.2	−24.4	−15.5	−17.1	−18.4	−24.1

.

8.1.1. Superior Drawdown Protection from Overnight Strategies

Strategy #1 (Long/Cash) demonstrates exceptional drawdown protection with MDDs ranging from $-7.7\%$ (XLU) to $-12.5\%$ (XLF), representing the shallowest drawdowns across all active strategies. These modest drawdowns—substantially smaller than the $-15.3\%$ to $-22.4\%$ experienced by buy-and-hold (Strategy #5)—indicate that overnight momentum strategies provide meaningful capital preservation during market crises. The superior drawdown performance stems from two factors: (1) reduced market exposure (holding cash for 6.5 h daily eliminates daytime volatility exposure), and (2) the persistence of overnight positive drift even during bear markets, as negative news tends to be processed gradually rather than creating sustained negative overnight gaps.

The drawdown advantage is most pronounced in Utilities (Strategy #1: $-7.7\%$ vs. Strategy #5: $-15.8\%$, representing 51% drawdown reduction) and Consumer Staples ($-8.4\%$ vs. $-12.4\%$, 32% reduction). These defensive sectors demonstrate that overnight momentum strategies particularly excel at capital preservation in sectors with stable fundamentals, where overnight gaps reflect information processing rather than panic selling.

Conversely, Strategy #2 (Short/Cash) exhibits substantially deeper drawdowns ($-12.8\%$ to $-20.6\%$) than its long counterpart, confirming that shorting overnight momentum not only generates losses but exposes investors to severe drawdown risk during market rallies. The asymmetry between long and short drawdowns (e.g., XLK: $-12.1\%$ long vs. $-20.6\%$ short) validates the persistent positive overnight drift documented in previous sections.

8.1.2. Daytime Strategy Drawdown Vulnerability

Pure daytime strategies (Strategies #3, #4) show deeper drawdowns ($-13.5\%$ to $-22.1\%$) than overnight strategies, with Strategy #3 (Cash, Long) particularly vulnerable in Energy ($-22.1\%$), Financials ($-20.0\%$), and Technology ($-20.0\%$). These severe drawdowns reflect the concentration of panic selling and forced liquidation during regular trading hours when market stress peaks. Major market crashes typically feature extreme intraday volatility with circuit breakers triggered during trading hours rather than through overnight gaps.

The daytime short strategy (Strategy #4) shows comparable or slightly smaller drawdowns than daytime long in some sectors (e.g., XLU: $-15.8\%$ vs. $-17.6\%$), suggesting that shorting during the day provides modest protection during certain crisis periods when daytime declines dominate. However, the overall negative returns of this strategy (documented in Section 4) indicate that the occasional drawdown benefits do not compensate for systematic losses during normal market conditions.

8.1.3. Buy-and-Hold Drawdown Experience

Strategy #5 (Long/Long) exhibits MDDs ranging from $-12.4\%$ (XLP) to $-22.4\%$ (XLE), representing the typical drawdown experience for passive equity investors over the 1999–2024 period. These drawdowns, while substantial, remain well below the maximum historical S&P 500 drawdowns of approximately $-50\%$ during the 2008 financial crisis, because our yearly average MDD metric captures typical annual worst declines rather than the absolute worst historical drawdown.

The cross-sectional pattern reveals sector-specific crisis vulnerabilities: Energy ($-22.4\%$), Technology ($-20.7\%$), and Financials ($-20.9\%$) experienced the deepest drawdowns, reflecting their high sensitivity to economic cycles, while Consumer Staples ($-12.4\%$) and Healthcare ($-14.6\%$) provided superior defensive characteristics. This sector differentiation validates standard portfolio theory regarding defensive versus cyclical equity exposure during market stress.

Notably, Strategy #1 (overnight only) outperforms buy-and-hold on drawdown metrics in all ten sectors, with improvements ranging from 18% (XLY) to 51% (XLU). This consistent reduction in drawdown, combined with comparable or superior absolute returns documented earlier, suggests that overnight momentum strategies offer a genuine improvement in risk–return profiles beyond what standard Sharpe ratio analysis reveals.

8.1.4. Extreme Drawdown Risk in Short and Contrarian Strategies

Short strategies exhibit catastrophic drawdown risk across all variations. Strategy #6 (Short/Short) shows MDDs from $-17.5\%$ (XLP) to $-28.5\%$ (XLE), representing 36–41% deeper drawdowns than buy-and-hold. Strategy #7 (Short/Long), which shorts overnight and goes long during the day, suffers even worse drawdowns ($-19.6\%$ to $-30.1\%$), with Energy reaching $-30.1\%$—effectively eliminating nearly one-third of capital during the worst annual decline.

The catastrophic performance of short strategies reflects their exposure to unlimited upside risk during strong market rallies, particularly the extended bull markets of 2003–2007, 2009–2020, and 2020–2024 recovery periods. During these rallies, persistent overnight positive drift compounds losses for short positions, creating severe drawdowns that overwhelm any gains during brief bear markets.

Strategy #19 (Short, Inertia) demonstrates the most extreme drawdown risk, with MDDs reaching $-33.4\%$ (XLK) and $-31.5\%$ (XLF). These devastating drawdowns—representing permanent capital losses exceeding 30%—confirm that combining short exposure with momentum signals creates particularly dangerous risk profiles unsuitable for any investor risk tolerance level.

8.1.5. Dynamic Strategy Drawdown Patterns

Pure dynamic strategies show mixed drawdown performance depending on their construction. Strategy #13 (Inertia, Inertia) exhibits substantial drawdowns ($-17.9\%$ to $-26.1\%$), comparable to or exceeding buy-and-hold in most sectors. The deeper drawdowns in Consumer Staples ($-24.4\%$ vs. $-12.4\%$ for buy-and-hold) and Utilities ($-26.1\%$ vs. $-15.8\%$) are particularly concerning, as these defensive sectors should, in theory, provide stability. The poor drawdown performance reflects the strategy’s vulnerability during momentum reversals, when sustained directional moves suddenly shift, leading to consecutive losses in both sub-periods.

Strategy #14 (Inertia, Reversal) demonstrates more moderate drawdowns ($-14.4\%$ to $-25.7\%$), generally comparable to buy-and-hold. The combination of momentum and reversal positioning across sub-periods appears to provide some diversification benefit, reducing extreme drawdown risk compared to pure momentum approaches.

Strategy #16 (Reversal, Reversal) shows highly sector-dependent drawdown risk: exceptional protection in Consumer Staples ($-11.2\%$, better than buy-and-hold) but catastrophic losses in Energy ($-33.6\%$) and Materials ($-26.8\%$). This extreme variation confirms that mean-reversion strategies are effective only in sectors with strong valuation anchoring (defensive sectors), while failing dramatically in trending sectors (such as commodities and cyclicals).

8.1.6. Mixed Strategy Drawdown Performance

Strategy #18 (Long, Reversal) achieves favorable drawdown characteristics across most sectors, with MDDs ranging from $-11.6\%$ (XLP) to $-25.4\%$ (XLE). The strategy provides meaningful drawdown protection compared to buy-and-hold in eight of ten ETFs, with particularly strong protection in Consumer Staples ($-11.6\%$ vs. $-12.4\%$), Healthcare ($-14.5\%$ vs. $-14.6\%$), Utilities ($-16.7\%$ vs. $-15.8\%$), and Industrials ($-18.0\%$ vs. $-17.7\%$).

The superior drawdown performance of Strategy #18 relative to pure overnight momentum (Strategy #1) varies by sector. In some sectors, such as Energy ($-25.4\%$ vs. $-11.4\%$), the mixed strategy exhibits substantially deeper drawdowns, reflecting the strategy’s daytime reversal positioning working against persistent commodity-driven momentum. However, in most sectors, Strategy #18 achieves drawdowns only modestly worse than pure overnight exposure while generating substantially higher absolute returns, creating a favorable risk–return tradeoff.

Comparing Strategy #18 to buy-and-hold reveals that the mixed strategy provides comparable or superior drawdown protection across most sectors while delivering higher returns (as documented in Section 4) and better Sharpe ratios (as documented in Section 6). This combination—superior returns, better risk-adjusted performance, and comparable drawdowns—suggests that Strategy #18 represents a genuine improvement over passive alternatives for investors with access to low-cost trading.

8.1.7. Sector-Specific Drawdown Characteristics

Cross-sectional drawdown analysis reveals fundamental differences in sector crisis behavior:

• Consumer Staples (XLP): Exhibits the shallowest drawdowns across most strategies ($-7.7\%$ to $-24.4\%$), with Strategy #1 achieving exceptional $-8.4\%$ MDD and Strategy #12 (Reversal/Cash) reaching an extraordinary $-7.7\%$. This defensive sector’s stable demand and pricing power provide natural crisis protection, making it ideal for drawdown-sensitive strategies.
• Utilities (XLU): Shows similarly strong drawdown protection ($-7.7\%$ to $-28.5\%$), with Strategy #1 achieving the best overall drawdown performance at $-7.7\%$. The sector’s regulated cash flows and bond-like characteristics create stability during periods of equity market stress, although the sector remains vulnerable to interest rate shocks.
• Energy (XLE): Demonstrates the deepest drawdowns across most strategies ($-11.4\%$ to $-33.6\%$), with Strategy #16 (Reversal/Reversal) suffering catastrophic $-33.6\%$ losses. The sector’s commodity price sensitivity creates extreme volatility during both boom–bust oil cycles and broader market crises, making it unsuitable for drawdown-sensitive investors despite strong momentum returns during normal periods.
• Financials (XLF): Exhibits severe drawdowns particularly for contrarian strategies ($-31.3\%$ for Strategy #15), reflecting the sector’s leverage effects and credit cycle sensitivity. The 1999–2024 period encompasses the 2008 financial crisis, during which financial stocks experienced near-total collapse, resulting in extreme historical drawdowns that contaminate average MDD metrics.
• Technology (XLK): Shows moderate-to-severe drawdowns ($-12.1\%$ to $-33.4\%$) depending on strategy, with pure overnight positioning ($-12.1\%$) providing exceptional protection despite the dot-com crash within the study period. The sector’s growth characteristics create substantial drawdown risk during broader market declines, though individual company strength can provide some resilience.
• Healthcare (XLV): Demonstrates favorable drawdown characteristics ($-9.6\%$ to $-28.0\%$), with overnight strategies particularly effective ($-9.6\%$). The sector’s defensive earnings characteristics and innovation-driven growth create a balanced profile suitable for various strategic approaches.

8.1.8. Drawdown Recovery Implications

The magnitude of maximum drawdowns has critical implications for recovery time and compound growth. A $-20\%$ drawdown requires a $+25\%$ return to break even, while a $-30\%$ drawdown requires $+43\%$, and a $-50\%$ drawdown requires $+100\%$. The mathematical asymmetry of drawdown recovery means that strategies with shallower drawdowns (Strategy #1: $-7.7\%$ to $-12.5\%$, requiring only 8–14% gains for recovery) can compound wealth more effectively than those with deeper drawdowns (Strategy #7: $-19.6\%$ to $-30.1\%$, requiring 24–43% gains for recovery).

This asymmetry explains why Strategy #1 achieves superior long-term compound returns despite having lower arithmetic mean returns than some higher-volatility strategies: shallow drawdowns enable faster recovery and uninterrupted compounding, whereas deep drawdowns can prolong recovery and prevent uninterrupted compounding.

For institutional investors, the depth of drawdown also impacts leverage capacity and risk management. Strategies with typical drawdowns of $-8\%$ to $-12\%$ (Strategy #1) can potentially employ 2–3 times leverage while maintaining acceptable risk levels, whereas strategies with drawdowns of $-20\%$ to $-30\%$ become unsuitable for leveraged implementation due to margin call risk and position liquidation during stress periods.

8.1.9. Comparison with Transaction Cost Analysis

Integrating the drawdown findings with the transaction cost analysis from Section 5 reveals that drawdown protection offers a key advantage that persists even when transaction costs eliminate absolute profitability. At 2 bps transaction costs, Strategy #1 generates minimal absolute returns but still provides $-8.7\%$ to $-12.5\%$ drawdown protection compared to $-15.3\%$ to $-22.4\%$ for buy-and-hold. This suggests that even investors facing costs that eliminate alpha generation might still benefit from overnight momentum strategies purely for downside protection, treating the strategy as a defensive rather than return-seeking approach.

However, at 3+ bps, where all strategies become unprofitable (as documented in Section 5), the drawdown benefits may not justify implementation complexity and trading costs. The strategic implication is that investors facing 1–2 bps costs should consider overnight momentum primarily for capital preservation, while those facing 3+ bps should default to buy-and-hold despite accepting deeper drawdowns as the cost of avoiding friction.

8.1.10. Practical Implications for Risk Management

The maximum drawdown analysis provides several critical insights for strategy implementation and risk management:

1.

Overnight strategies offer genuine downside protection: Strategy #1’s 18–51% drawdown reduction compared to buy-and-hold represents a meaningful risk benefit beyond Sharpe ratio improvements, particularly valuable for investors with low drawdown tolerance or those approaching retirement needing capital preservation.

2.

Short strategies expose investors to catastrophic risk: the $-20\%$ to $-33\%$ drawdowns documented for short strategies represent unacceptable risk levels that cannot be justified by any potential return benefits, confirming these strategies should be universally avoided.

3.

Sector selection critically impacts drawdown risk: concentrating strategies in defensive sectors (XLP, XLU) provides substantial drawdown protection, while exposure to cyclical sectors (XLE, XLF) creates vulnerability to severe losses during crises.

4.

Mixed strategies balance returns and drawdowns: Strategy #18 achieves favorable drawdown characteristics ($-11.6\%$ to $-25.4\%$) while generating superior returns, suggesting this approach provides an optimal risk–return combination for most investor profiles.

The maximum drawdown analysis confirms that overnight momentum strategies provide not only superior returns and Sharpe ratios but also meaningful downside protection during market crises, with drawdown reductions of 18–51% compared to buy-and-hold across most sectors. This triple advantage—higher returns, better risk-adjusted performance, and shallower drawdowns—establishes overnight momentum as a genuinely superior investment approach for low-cost institutional traders. Meanwhile, the catastrophic drawdowns of short and contrarian strategies confirm that these approaches should be avoided, regardless of their theoretical appeal.

• Section Summary. Strategy #1 provides the best drawdown protection of any active strategy (−10.4% average MDD vs. −17.8% for buy-and-hold), a 42% improvement. Strategy #18 achieves comparable drawdowns to buy-and-hold while generating substantially higher returns. Short strategies carry catastrophic drawdown risk (−20% to −33%) and should be avoided. Defensive sectors (XLP, XLU) show the shallowest drawdowns, while commodity-linked sectors (XLE, XLF) show the deepest.

9. Summary Statistics Averaged Across All ETFs

9.1. Aggregate Performance Metrics

To synthesize the comprehensive sector-by-sector analysis presented in previous sections, we now examine aggregate performance metrics averaged across all ten ETFs. This cross-sectional averaging reveals which strategies demonstrate robust performance across diverse market segments versus those that succeed only in specific sectors. Table 14, Table 15, Table 16 and

Table 17. Average yearly Sortino ratio by strategy and ETF. Blue color in Strategy #5 indicates the Sortino ratio for the passive Buy&Hold (long, long) strategy. The green color indicates that the corresponding strategy has a higher Sortino ratio than the passive strategy. Finally, the red color indicates that the corresponding strategy has a lower Sortino ratio than the passive strategy.

#	Strategy		SPY	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY
	Overnight	Daytime
1	Long	Cash	1.50	1.34	1.57	1.46	1.51	1.43	0.76	2.11	1.25	1.08
2	Short	Cash	−2.29	−1.92	−2.13	−1.77	−2.18	−2.17	−1.63	−2.71	−2.14	−1.77
3	Cash	Long	0.14	−0.01	−0.26	−0.06	0.01	−0.05	0.22	−0.30	−0.07	0.30
4	Cash	Short	−0.72	−0.35	−0.08	−0.34	−0.44	−0.40	−0.85	−0.15	−0.36	−0.72
5	Long	Long	1.03	0.78	0.73	0.87	0.97	1.01	0.83	0.86	0.90	1.04
6	Short	Short	−1.59	−1.17	−1.06	−1.21	−1.43	−1.53	−1.43	−1.45	−1.41	−1.53
7	Short	Long	−0.89	−0.83	−1.16	−0.84	−0.99	−1.04	−0.33	−1.21	−0.79	−0.52
8	Long	Short	0.52	0.64	0.88	0.77	0.76	0.78	−0.07	0.89	0.56	0.27
9	Cash	Inertia	−0.29	0.16	0.52	−0.81	−1.16	−1.01	−1.91	−1.19	−1.23	−0.89
10	Cash	Reversal	−0.08	−0.55	−0.71	0.55	1.11	0.78	1.89	1.10	1.39	0.69
11	Inertia	Cash	−1.19	0.27	1.18	0.22	0.20	0.03	−1.33	−1.27	−0.22	−0.09
12	Reversal	Cash	0.53	−0.71	−1.48	−0.58	−0.72	−0.36	0.68	0.51	−0.12	−0.26
13	Inertia	Inertia	−0.62	0.39	1.16	−0.37	−0.77	−0.66	−1.92	−1.38	−0.92	−0.59
14	Inertia	Reversal	−0.40	−0.15	0.14	0.74	1.31	0.89	1.01	0.61	1.17	0.66
15	Reversal	Inertia	0.08	−0.15	−0.29	−0.83	−1.11	−0.87	−1.00	−0.63	−0.96	−0.79
16	Reversal	Reversal	0.35	−0.72	−1.31	0.32	0.74	0.53	2.22	1.50	1.27	0.50
17	Long	Inertia	0.71	0.96	1.31	0.30	0.10	0.22	−0.87	0.05	−0.10	0.02
18	Long	Reversal	1.00	0.41	0.34	1.62	2.05	1.89	2.33	2.23	2.42	1.47
19	Short	Inertia	−1.31	−0.72	−0.50	−1.50	−2.00	−1.87	−2.18	−2.02	−1.87	−1.57
20	Short	Reversal	−1.10	−1.32	−1.62	−0.48	−0.07	−0.53	0.90	−0.23	0.06	−0.37
21	Inertia	Long	−0.26	0.29	0.57	0.18	0.28	0.11	−0.33	−0.68	−0.00	0.37
22	Reversal	Long	0.47	−0.30	−0.88	−0.27	−0.26	−0.15	0.79	0.23	0.01	0.19
23	Inertia	Short	−0.88	0.01	0.72	0.06	−0.03	−0.09	−1.18	−0.55	−0.30	−0.44
24	Reversal	Short	−0.17	−0.54	−0.81	−0.45	−0.60	−0.44	−0.11	0.28	−0.24	−0.60

present the mean Sharpe ratio, Sortino ratio, volatility, and maximum drawdown for each of the 24 strategies, calculated by averaging the corresponding metrics across SPY, XLB, XLE, XLF, XLI, XLK, XLP, XLU, XLV, and XLY.

The Sortino ratio, which appears here for the first time, represents a refinement of the Sharpe ratio that penalizes only downside volatility rather than total volatility Sortino and Price (1994). It is calculated as follows:

$$\mathrm{Sortino}\mathrm{Ratio}={\displaystyle \frac{\overline{R}-R_f}{{\sigma }_d}}$$

(9)

where ${\sigma }_d$ is the standard deviation of negative returns only.

Sortino ratios for strategies are shown in Table 17.

9.1.1. Clear Performance Hierarchy

The aggregate metrics reveal a clear performance hierarchy across the 24 strategies, with Strategy #1 (Long, Cash) and Strategy #18 (Long, Reversal) emerging as the dominant approaches when averaged across all sectors. Strategy #1 achieves a mean Sharpe ratio of 0.95 and Sortino ratio of 1.40, representing the highest risk-adjusted performance among single sub-period strategies. Strategy #18 demonstrates even stronger performance with a mean Sharpe ratio of 0.87 and an exceptional Sortino ratio of 1.58, indicating superior downside risk management.

Buy-and-hold (Strategy #5) shows respectable aggregate performance with a Sharpe ratio of 0.61 and Sortino ratio of 0.90, serving as the baseline for comparison. The fact that Strategies #1 and #18 exceed buy-and-hold by 56% and 43%, respectively (in Sharpe ratio terms), confirms that tactical momentum positioning provides genuine alpha across diverse market segments rather than succeeding in only isolated sectors.

The worst-performing strategies are uniformly those involving short positions: Strategy #2 (Short, Cash): Sharpe $-1.38$, Strategy #19 (Short, Inertia): Sharpe $-1.11$, Strategy #6 (Short/Short): Sharpe $-0.85$, and Strategy #15 (Reversal, Inertia): Sharpe $-0.49$. The consistency of negative risk-adjusted returns across all short-based approaches validates the earlier conclusion that equity market drift is too persistent to profit from systematic shorting.

9.1.2. Overnight vs. Daytime Performance Gap

The aggregate statistics quantify the magnitude of the overnight–daytime performance differential documented in earlier sections. Strategy #1 (overnight long) achieves a 0.95 Sharpe ratio, while Strategy #3 (daytime long) generates $-0.01$, representing an effective 96-percentage-point advantage for overnight positioning. This stark contrast—where overnight strategies achieve near-1.0 Sharpe ratios, while daytime strategies barely break even—provides compelling evidence that exploitable momentum concentrates in non-trading hours.

The volatility differential reinforces this finding: overnight strategies exhibit 11.7% average volatility versus 17.1% for daytime strategies, a 46% increase. Combined with the Sharpe ratio advantage, this indicates that daytime periods yield both lower returns and higher volatility — a doubly unfavorable combination. The drawdown comparison (overnight: $-10.4\%$; daytime: $-17.7\%$) further confirms that overnight strategies provide superior risk management across all dimensions.

The consistency of this pattern—where every risk metric (Sharpe, Sortino, volatility, drawdown) favors overnight over daytime positioning—suggests that the overnight advantage represents a fundamental market characteristic rather than a statistical anomaly or data mining artifact. Additional statistics of overnight and daytime returns are presented in Appendix E.

9.1.3. Sortino Ratio Insights

The Sortino ratio analysis reveals important asymmetries in return distributions. Strategy #18 shows the largest Sortino-to-Sharpe differential (1.58 vs. 0.87, representing an 82% improvement), indicating this mixed strategy generates positively skewed returns with larger gains than losses. This positive skewness likely reflects the strategy’s ability to capture persistent overnight drift while avoiding large daytime losses through reversal positioning.

Strategy #1 similarly demonstrates positive skewness (Sortino 1.40 vs. Sharpe 0.95, a 47% improvement), confirming that overnight momentum creates favorable asymmetry with larger upside captures than downside exposures. This positive skewness represents an additional benefit beyond what the Sharpe ratio analysis reveals, as investors typically prefer return distributions with limited downside and uncapped upside.

Conversely, short strategies show even worse Sortino ratios than Sharpe ratios: Strategy #2 (Sortino $-2.07$ vs. Sharpe $-1.38$, 50% deterioration) and Strategy #19 (Sortino $-1.55$ vs. Sharpe $-1.11$, 40% deterioration). This negative asymmetry indicates these strategies suffer disproportionately large downside losses relative to any occasional gains, creating particularly unfavorable risk profiles for loss-averse investors.

Buy-and-hold (Strategy #5) shows moderate positive skewness (Sortino 0.90 vs. Sharpe 0.61, 48% improvement), consistent with the well-documented positive skewness of equity returns over long horizons. However, both Strategy #1 and Strategy #18 demonstrate superior Sortino ratios, indicating that tactical momentum approaches improve upon the natural positive skewness of equity markets.

9.1.4. Volatility Clustering by Strategy Type

The aggregate volatility metrics reveal clear clustering by strategy exposure patterns. Single-sub-period strategies exhibit the lowest volatilities: overnight-only strategies average 11.7–11.8%, while daytime-only strategies average 17.0–17.1%. Full-cycle strategies cluster at higher levels: buy-and-hold and dynamic strategies average 20.4–21.3%, with minimal variation across different position rules (momentum, reversal, mixed).

This volatility clustering by exposure duration rather than strategy logic (momentum vs. reversal) indicates that volatility is primarily determined by market participation time rather than positioning decisions. Whether following momentum or betting against it, investors participating in both sub-periods face approximately 20–21% annualized volatility, while those trading during only one sub-period experience proportionally reduced volatility based on their exposure fraction.

The practical implication is that investors seeking volatility reduction should focus on exposure duration (trading only overnight) rather than strategy sophistication (complex dynamic rules), as the former provides a dramatic reduction in volatility (11.7% vs. 20.4%, a 43% decrease), while the latter offers minimal impact.

9.1.5. Drawdown Hierarchy

The aggregate maximum drawdown statistics reveal a clear protective hierarchy (Magdon Ismail et al. 2004). Strategy #1 (overnight long) provides the best drawdown protection at $-10.4\%$ average MDD, followed by Strategy #11 (Inertia, Cash) at $-12.2\%$ and Strategy #12 (Reversal, Cash) at $-14.0\%$. All overnight-only strategies demonstrate superior drawdown protection compared to buy-and-hold’s $-17.8\%$ average MDD.

Full-cycle strategies show consistently deeper drawdowns, ranging from $-17.8\%$ (buy-and-hold) to $-27.6\%$ (Short, Inertia). Strategy #18, despite its superior Sharpe and Sortino ratios, exhibits $-18.2\%$ average MDD—marginally worse than buy-and-hold but still among the better full-cycle strategies. This suggests that the mixed strategy’s superior performance primarily stems from enhanced returns rather than drawdown protection.

Short strategies universally demonstrate catastrophic drawdown risk, with Strategy #19 (Short, Inertia) averaging $-27.6\%$, Strategy #15 (Reversal/Inertia) $-25.6\%$, and Strategy #7 (Short, Long) $-25.8\%$. These severe drawdowns—representing more than one-quarter loss of capital during typical worst annual declines—confirm that short-based approaches expose investors to unacceptable tail risk regardless of any theoretical return potential.

9.1.6. Optimal Strategy Selection Framework

The aggregate metrics enable the construction of a clear strategy selection framework based on investor objectives:

For maximum risk-adjusted returns with moderate exposure: Strategy #1 (Long, Cash) offers the optimal combination of Sharpe ratio (0.95), Sortino ratio (1.40), low volatility (11.7%), and exceptional drawdown protection ($-10.4\%$). This strategy suits investors seeking overnight momentum exposure while preserving capital, accepting reduced market participation in exchange for superior risk-adjusted performance.

For maximum absolute returns with full market exposure: Strategy #18 (Long, Reversal) delivers the best Sortino ratio (1.58) and strong Sharpe ratio (0.87) among full-cycle strategies, with acceptable drawdowns ($-18.2\%$) comparable to buy-and-hold. This strategy suits institutional investors with low transaction costs seeking to outperform passive benchmarks while maintaining continuous market exposure.

For passive benchmark with minimal trading: Strategy #5 (Long, Long) provides moderate risk-adjusted returns (Sharpe 0.61, Sortino 0.90) with no ongoing trading costs, representing the default choice for high-cost retail investors or those preferring simplicity over optimization.

Strategies to avoid universally: all short-based strategies (Strategies #2, #6, #7, #19, #20) demonstrate deeply negative Sharpe ratios, severe drawdowns, and negative skewness, making them unsuitable for any investor profile regardless of risk tolerance or investment horizon.

9.1.7. Performance Robustness Across Sectors

The aggregation methodology — simple averaging across 10 diverse ETFs spanning defensive, cyclical, growth, and commodity sectors — provides confidence in the strategy’s robustness. Strategies achieving strong aggregate metrics (like #1 and #18) succeed not through exceptional performance in a single sector but through consistent positive performance across multiple market segments.

This broad-based success contrasts with sector-specific strategies like Strategy #13 (Inertia, Inertia), which achieved exceptional results in Energy but failed in most other sectors, resulting in a weak aggregate Sharpe ratio of $-0.46$. The poor aggregate performance, despite the highest single-sector return (XLE: 12,882%), confirms that sector concentration creates unacceptable risk unless investors have strong conviction and can tolerate extended periods of underperformance.

Strategy #18’s strong aggregate Sharpe ratio (0.87), despite substantial cross-sectional variation (from 0.17 in XLE to 1.25 in XLU), indicates genuine robustness—the strategy succeeds in most sectors even though optimal sector allocation would further improve performance. This robustness makes Strategy #18 suitable for diversified portfolio implementation rather than requiring concentrated sector bets.

9.1.8. Comparison with Academic Literature

The documented Sharpe ratios compare favorably with academic literature on momentum strategies. Traditional monthly momentum strategies typically achieve Sharpe ratios of 0.4–0.6, while weekly momentum strategies achieve Sharpe ratios of 0.5–0.7. Our Strategy #1 (0.95 Sharpe) and Strategy #18 (0.87 Sharpe) exceed these benchmarks, suggesting that intraday temporal decomposition (overnight vs. daytime) captures momentum effects more efficiently than traditional calendar-based approaches.

The superior performance likely stems from temporal decomposition aligning with natural information-processing cycles: overnight gaps reflect discrete information arrival that creates predictable price adjustments, while traditional approaches that ignore these sub-daily patterns may dilute signals by mixing strong overnight drift with noisy daytime movements, thereby reducing overall strategy efficiency.

However, direct comparison requires caution, as our strategies operate on sector ETFs rather than individual stocks, trade daily rather than monthly/weekly, and measure performance over a specific 25-year period (1999–2024) rather than the longer horizons typically examined in academic studies. The favorable comparison nonetheless suggests that overnight momentum represents a promising avenue for momentum research beyond traditional approaches.

9.1.9. Practical Implementation Considerations

While the aggregate metrics demonstrate Strategy #1 and Strategy #18 superiority, practical implementation requires consideration of several factors:

Transaction costs: As documented in Section 5, costs above 2–3 bps eliminate profitability for most active strategies. The aggregate metrics represent zero-cost theoretical performance, meaning institutional investors with sub-1 bp costs can fully realize these advantages, while retail investors facing 3+ bps costs should default to Strategy #5 (buy-and-hold) despite inferior risk-adjusted metrics.

Execution complexity: Strategy #1 requires approximately 13,000 trades over the 25-year period (buying at close, selling at open daily), while Strategy #18 involves approximately 14,400 trades with dynamic daytime positioning. Institutional investors with automated execution systems can implement these strategies efficiently, whereas retail investors may face operational challenges and errors that can erode their performance.

Tax implications: For taxable accounts, the frequent trading inherent in Strategies #1 and #18 generates short-term capital gains taxed at ordinary income rates, potentially eliminating after-tax alpha for high-bracket investors. Strategy #5 (buy-and-hold) benefits from low, as momentum-reversal decisions require reallocation, providing substantial tax advantages that partially offset pre-tax performance differences.

Psychological factors: Strategy #1’s overnight-only positioning requires daily discipline to sell at open and repurchase at close, creating behavioral challenges for discretionary traders. Strategy #18’s dynamic daytime positioning adds further complexity with momentum-reversal decisions requiring strict rule adherence. Automated execution eliminates these behavioral risks, but it requires significant infrastructure investment.

The aggregate performance metrics confirm that overnight momentum strategies, particularly Strategy #1 (Long/Cash) and Strategy #18 (Long/Reversal), deliver superior risk-adjusted returns across diverse market sectors when implementation frictions are minimal. The consistency of results across multiple risk metrics (Sharpe, Sortino, volatility, and drawdown) and diverse sectors (defensive, cyclical, growth, and commodity) validates that overnight momentum represents a genuine market inefficiency that can be exploited by sophisticated institutional investors with appropriate cost structures and execution capabilities.

• Total Trades = cumulative number of position changes over 6782 trading days (1999–2025).
• Trades/Day = average daily trading frequency (maximum possible = 4).
• Buy & Hold strategies ((Long, Long) and (Short, Short)) require only 1 trade (initial entry).
• Static opposite strategies ((Long, Short) and (Short, Long)) require 4 trades/day (always flip positions).
• Dynamic strategies (Inertia, Reversal) have variable trade frequency depending on signal alignment.
• Final values averaged across 10 sector ETFs (SPY, XLB, XLE, XLF, XLI, XLK, XLP, XLU, XLV, XLY).

• Section summary: Aggregating across all ten ETFs, Strategy #1 leads on risk-adjusted performance (Sharpe 0.95, Sortino 1.40, MDD −10.4%), while Strategy #18 leads on absolute return (Sortino 1.58). Both exceed buy-and-hold (Sharpe 0.61) consistently across defensive, cyclical, growth, and commodity sectors. The consistency across diverse sectors—not performance in a single sector—is the primary evidence of robustness.

10. Strategy Classification by Trading Intensity

10.1. Trading Frequency and Viability Analysis

Beyond risk-adjusted performance metrics, the practical viability of trading strategies depends critically on their trading frequency and resulting transaction cost exposure.

Table 18. Strategy classification by trading intensity.

Category	Strategies	Trades/Day	Gross Return	Net (2bps)
Zero Trading	(Long, Long), (Short, Short)	0.00	(749, 4)	(749, 4)
Low (1.8/day)	(Long, Inertia), (Short, Reversal)	1.80	(2034, 125)	(188, 11)
Medium (2.0/day)	Single-session strategies	2.00	64–106	5–118
High (2.2/day)	(Long, Reversal), (Short, Inertia)	2.20	(13,856, 3)	(775, 0)
Maximum (4.0/day)	(Long, Short), (Short, Long)	4.00	(132, 5)	(9, 0)

Key insight: At realistic transaction costs (2+ bps), Buy & Hold (Long, Long) becomes the dominant strategy because it requires no ongoing trading. High-frequency strategies like (Long, Reversal) show impressive gross returns but are economically unviable after transaction costs.

presents a classification framework that groups strategies by their average daily trade frequency, showing how transaction costs transform theoretical performance into realized returns. Using SPY as a representative example, we demonstrate the dramatic impact of trading intensity on strategy viability under realistic cost assumptions.

10.2. Results and Discussion

10.2.1. The Zero-Trading Advantage

The most fundamental insight from the trading intensity classification is the overwhelming advantage of zero-trading strategies under realistic transaction cost regimes. Buy-and-hold (Long, Long) maintains identical gross and net returns ($749 in SPY) because it requires only a single initial trade over the entire 25-year period, incurring effectively zero ongoing transaction costs. This immunity to friction costs becomes increasingly valuable as trading frequency rises across other strategy categories.

The contrast between zero-trading and even low-frequency strategies is stark: Strategy #1 (Long/Cash), classified as “Medium” with 2.0 trades per day, achieves impressive gross returns of $774 in SPY but faces approximately 13,078 trades over the study period (Table 17). At 2 bps per trade, this generates cumulative friction costs that reduce net returns to $57—a 93% wealth destruction despite strong underlying momentum effects.

This dramatic deterioration in performance validates the central thesis that market inefficiencies, while genuine, remain exploitable only within narrow cost regimes. The zero-trading category represents the only approach immune to the compounding friction effects documented in Section 5, explaining why passive indexing dominates retail investment despite the existence of exploitable momentum patterns.

10.2.2. Low-Frequency Strategies: Conditional Viability

Strategies averaging 1.8 trades per day—primarily mixed approaches combining static overnight positioning with conditional daytime signals ((Long, Inertia) Strategy #17, (Short, Reversal): Strategy #20)—demonstrate strong gross returns ($2034 for (Long, Inertia)) but experience severe friction erosion. At 2 bps costs, (Long, Inertia) nets only $188, representing 91% wealth destruction, while (Short, Reversal) deteriorates from $125 gross to $11 net.

The classification as “low” frequency (1.8 trades/day vs. 2.0+ for most active strategies) reflects these strategies’ conditional daytime positioning: they avoid trading when momentum signals do not trigger, resulting in a modest reduction in frequency. However, this reduction proves insufficient to preserve profitability under 2 bps costs, as the ${(1-\alpha )}^{Nk}$ friction multiplier with $k=1.8$ and $N=6750$ still generates approximately 70% wealth erosion.

The practical implication is that reducing trading frequency from 2.0 to 1.8 trades/day provides marginal cost savings but fails to cross the viability threshold. Strategies require either zero trading (buy-and-hold) or a dramatic reduction in trading frequency (to 0.5 trades/day or less) to maintain profitability under retail cost structures above 2 bps.

10.2.3. Medium-Frequency Strategies: The Standard Active Approach

The medium-frequency category encompasses most single-session strategies (overnight-only or daytime-only) and averages exactly 2.0 trades per day: one entry and one exit per session. This category includes Strategy #1 (Long, Cash), Strategy #3 (Cash, Long), and their short/reversal variations, representing the canonical active momentum approach with daily position rebalancing.

Gross returns within this category vary dramatically ($64 to $1606 in SPY), reflecting the underlying strategy logic (momentum vs. reversal, overnight vs. daytime). However, net returns converge to a narrow band ($5 to $118), demonstrating that trading frequency dominates strategy selection under realistic costs—the friction multiplier overwhelms differences in gross return generation.

Strategy #1 (Long/Cash) exemplifies this category: gross returns of $774 deteriorate to $209 at 1 bp costs and $57 at 2 bps costs, with profitability eliminated entirely above 3 bps. This performance trajectory confirms that medium-frequency strategies occupy a narrow viability window between 0 and 2 bps, accessible only to institutional investors with sophisticated execution systems and direct market access.

The category’s heterogeneous gross returns but homogeneous net returns suggest that investors should focus first on achieving low-cost execution (accessing the 0–1 bp regime) before optimizing strategy selection within the medium-frequency category. Without sub-2 bp costs, strategy choice becomes irrelevant as all medium-frequency approaches fail.

10.2.4. High-Frequency Strategies: Gross Return Excellence, Net Return Failure

Strategies averaging 2.2 trades per day—primarily Strategy #18 (Long, Reversal) and Strategy #19 (Short, Inertia)—represent the “high” frequency category, distinguished by their dynamic positioning in both sub-periods with slightly elevated trading due to signal-driven adjustments. Strategy #18 achieves extraordinary gross returns ($13,856 in SPY, representing a 13,756% gain), reflecting its optimal combination of overnight momentum capture with daytime reversal exploitation.

However, the 10% increase in trading frequency relative to medium-frequency strategies (2.2 vs. 2.0 trades/day) results in disproportionate performance erosion under transaction costs. At 2 bps, Strategy #18 nets $775—a 94% decline from gross returns despite representing only modest additional trading activity. This nonlinear sensitivity reflects the exponential nature of compounding friction: ${(1-0.0002)}^{2.2\times 6750}$ versus ${(1-0.0002)}^{2.0\times 6750}$ represents the difference between 23% and 26% survival rates, a meaningful proportional gap.

The key insight is that increases in marginal trading frequency create disproportionate viability challenges. Moving from 2.0 to 2.2 trades per day—a mere 10% increase—reduces net wealth by an additional 77% beyond the standard medium-frequency erosion. This nonlinearity explains why high-frequency strategies, despite demonstrating superior gross returns through sophisticated signal combination, cannot justify their complexity under realistic costs.

Strategy #19 (Short, Inertia) shows even more dramatic deterioration, with gross returns of $3 becoming effectively $0 net of costs. The combination of negative expected returns (from shorting persistent positive drift) and elevated trading frequency creates a doubly negative scenario, in which friction costs eliminate any occasional profits that might arise from favorable momentum periods.

10.2.5. Maximum-Frequency Strategies: Theoretical Interest Only

Strategies averaging 4.0 trades per day—representing the maximum possible frequency with entry/exit in both sub-periods ((Long, Short): Strategy #8, (Short, Long): Strategy #7)—serve primarily as theoretical benchmarks demonstrating the limits of tactical positioning. These strategies switch between long and short positions twice daily, executing at close (for overnight positions), open (closing overnight and entering daytime), and close again (exiting daytime), resulting in four daily trades.

Strategy #8 (Long, Short) achieves respectable gross returns ($1732 in SPY) by capturing overnight positive drift while avoiding daytime exposure through short positioning. However, the 4.0 trades/day frequency generates catastrophic friction erosion: net returns collapse to $9 at 2 bps costs, representing 99.5% wealth destruction. The friction multiplier ${(1-0.0002)}^{4.0\times 6750}\approx 0.006$ indicates that strategies must achieve 16,700% gross returns merely to break even—an impossible threshold.

Strategy #7 (Short, Long) demonstrates even worse characteristics, with minimal gross returns ($5) becoming $0 net of costs. The combination of fighting overnight momentum (via short positioning) and excessive trading frequency creates a strategy that would require impossibly large daytime gains to overcome overnight losses and friction costs.

The practical conclusion is that maximum-frequency strategies are economically unviable under any realistic cost structure, including institutional rates. Even at 0.5 bps—well below typical institutional execution costs—Strategy #8 would face ${(1-0.00005)}^{27,000}\approx 0.26$ friction multiplier, eliminating 74% of wealth and rendering the strategy unprofitable. These approaches serve only as academic exercises demonstrating the theoretical limits of temporal arbitrage.

10.2.6. The Transaction Cost Viability Threshold

Synthesizing across trading intensity categories reveals a clear viability hierarchy:

• 0.00 trades/day (Buy-and-hold): viable at any cost structure; becomes dominant above 2–3 bps
• 1.80 trades/day (Low frequency): viable only below 1.5 bps; marginal improvement over medium frequency insufficient to justify complexity
• 2.00 trades/day (Medium frequency): viable below 2 bps; represents standard institutional active strategy
• 2.20 trades/day (High frequency): viable below 1 bp; requires exceptional execution quality and sophisticated infrastructure
• 4.00 trades/day (Maximum frequency): never economically viable under realistic conditions

This hierarchy demonstrates that transaction cost sensitivity increases nonlinearly with trading frequency. The gap between buy-and-hold (0.00) and medium frequency (2.00) represents a fundamental discontinuity—strategies either trade actively (2+ times daily) or not at all, with intermediate frequencies providing minimal advantage.

10.2.7. Optimal Strategy Selection Under Cost Constraints

The trading intensity framework enables clear strategy selection guidance based on investor cost structure:

For investors with 0–1 bp costs (large institutions, market makers):

• Primary: Strategy #18 (Long/Reversal, 2.2/day) for maximum gross return generation.
• Alternative: Strategy #1 (Long/Cash, 2.0/day) for superior drawdown protection.
• Rationale: high-frequency strategies remain viable; optimize for gross return generation.

For investors with 1–2 bp costs (mid-size institutions, active managers):

• Primary: Strategy #1 (Long/Cash, 2.0/day) balancing returns and costs.
• Alternative: Strategy #5 (Long/Long, 0.00/day) as friction approaches 2 bp.
• Rationale: medium-frequency strategies marginal; transition toward passive as costs rise.

For investors with 2+ bp costs (retail, small institutions):

• Primary: Strategy #5 (Long/Long, 0.00/day) exclusively.
• Alternative: none viable; all active strategies fail above 2–3 bps.
• Rationale: zero-trading approaches required; active strategies are economically irrational.

This cost-based framework explains the bifurcation of investment approaches in practice: institutional investors with sophisticated execution employ active momentum strategies, while retail investors default to passive indexing. Both approaches are rational given their respective cost structures, with the transaction cost viability threshold (2–3 bps) serving as the natural dividing line.

10.2.8. Implications for Market Efficiency

The trading intensity analysis provides insight into why momentum anomalies persist despite widespread knowledge of them. Exploiting overnight momentum requires:

1.

Sub-2 bp execution costs: achievable only with direct market access, sophisticated algorithms, and substantial scale

2.

Daily rebalancing discipline: requiring automated systems to eliminate behavioral errors and timing mistakes

3.

Infrastructure investment: trading platforms, execution systems, and risk management capabilities represent fixed costs viable only at an institutional scale

These barriers create a natural equilibrium where the anomaly persists because most investors cannot profitably exploit it. Retail investors facing 3–5 bp costs rationally avoid overnight momentum strategies despite their genuine positive expected returns, allowing the inefficiency to persist for the minority of institutional investors operating below the cost threshold.

This “limited access” equilibrium reconciles efficient market theory with exploitable anomalies: markets can be simultaneously efficient for most participants (retail investors) and inefficient for a minority (low-cost institutions), with transaction costs serving as the natural barrier maintaining this equilibrium.

10.2.9. Evolution of Trading Technology and Cost Implications

The historical trend toward lower transaction costs—driven by electronic trading, algorithmic execution, and exchange competition—has implications for the viability of momentum strategies. If institutional execution costs continue to decline from current 0.5–1.5 bps levels toward 0.25–0.75 bps, previously marginal high-frequency strategies (2.2 trades/day) would become viable for a broader institutional investor base.

However, this democratization would likely reduce momentum profitability by increasing arbitrage activity, creating a self-correcting mechanism in which lower costs enable exploitation, which in turn reduces gross returns, eventually restoring equilibrium at lower profit margins. The overnight momentum effect may persist, but with a diminished magnitude, requiring even more sophisticated approaches to generate alpha.

For retail investors, the cost threshold remains firmly above 2–3 bps despite zero-commission trading, as bid-ask spreads, market impact costs, and operational inefficiencies maintain total trading costs at levels that eliminate momentum strategy viability. The persistent retail cost disadvantage explains why passive indexing continues expanding despite decades of academic research documenting exploitable anomalies.

The trading intensity classification confirms that strategy viability depends primarily on trading frequency and investor cost structure rather than strategy sophistication or gross return potential. Buy-and-hold dominates above 2–3 bps regardless of active strategy performance, while medium- and high-frequency momentum approaches remain viable only for institutional investors achieving sub-2 bp execution costs. This framework offers practical guidance for selecting strategies based on investor-specific cost structures and explains the rational coexistence of active institutional trading and passive retail investing within the same markets.

11. Concluding Remarks

For practitioners and institutional investors, overnight inertial strategies may offer valuable alpha-generation opportunities and portfolio diversification benefits, particularly for institutions with low transaction costs, advanced execution systems, sufficient capital to withstand extended drawdowns, and sophisticated risk management capabilities. The combined (long, reversal) and (long, inertia) strategy appears particularly promising as it consistently generated superior risk-adjusted returns across multiple sectors while diversifying momentum sources across both temporal segments. These strategies appear most suitable for sophisticated institutional investors with comprehensive risk management capabilities, rather than individual investors or smaller institutions that lack the necessary infrastructure, risk tolerance, and capital reserves.

Implications for institutional managers, market regulation, and strategy design: For institutional portfolio managers operating below the 1–2 bps cost threshold, the overnight long component of Strategy #18 is implementable via market-on-close and market-on-open orders at minimal market impact, and the strategy’s Sharpe ratios of 0.87–1.25 across sectors compare favourably with most documented systematic equity strategies. The strategy is compatible with a passive-core/active-satellite architecture in which overnight positioning supplements a buy-and-hold core. From a regulatory perspective, our finding that the overnight premium is exploitable by low-cost institutions but not by retail investors (for whom costs exceed the viability threshold of 2–3 bps) raises questions about equitable access to market anomalies and potential policy interventions such as improved retail access to closing-auction mechanisms. For quantitative strategy designers, two design principles emerge from our analysis: (i) temporal decomposition into overnight and daytime sub-periods is the critical structural choice—applying identical signals to undivided 24 h returns produces approximately 80× less terminal wealth (see Section 11); and (ii) the reversal signal should use a single-lag lookback—extending to $k\ge 3$ periods degrades performance by a factor of 5–10 (see Appendix I).

Out-of-sample robustness: Because all 24 strategies are purely rule-based and contain no fitted parameters, there is no risk of in-sample overfitting in the conventional sense. The stationary bootstrap analysis in Appendix G serves as a principled substitute for a rolling-window out-of-sample test: by evaluating strategy performance on 1000 alternative simulated histories drawn from the observed data, it is demonstrated that Strategy #18 outperforms buy-and-hold in >95% of replications for six of ten ETFs. The consistency of our findings with prior independent literature on overnight returns (Berkman et al. 2012; Kelly and Clark 2011; Lou et al. 2019; Zhang and Pinsky 2025b) across different samples and time periods further supports external validity.

Our results are consistent with the overnight return literature (Berkman et al. 2012; Kelly and Clark 2011; Lou and Polk 2022; Lou et al. 2019), confirming that a large fraction of equity market returns is earned overnight rather than during the trading day. The transaction cost analysis aligns with findings (Frazzini et al. 2018; Novy-Marx and Velikov 2016) that implementation costs represent a binding constraint on anomaly exploitation. Our results also highlight the importance of further study of stock return dynamics (Cooper et al. 2008). Recent machine learning approaches to momentum and reversal trading (Li and Tam 2018; Wang et al. 2024) suggest promising directions for future research. Related algorithmic trading research (Valath and Pinsky 2023; Zhang and Pinsky 2025a) provides complementary perspectives on strategy optimization.

The findings make a significant contribution to the academic literature on market microstructure, behavioral finance, and systematic trading strategies, providing actionable insights for investors seeking to exploit persistent market inefficiencies through disciplined, systematic approaches to momentum investing in ETF markets. This research supports the continued relevance of active management strategies in an increasingly efficient market environment, highlighting the importance of understanding temporal patterns in price behavior for successful strategy implementation.

The sector-specific analysis reveals that overnight momentum strategies are not universally effective but rather exhibit substantial performance variation across sectors, driven by sensitivity to overnight news, global market connections, regulatory environments, and fundamental business characteristics. This finding suggests that sophisticated investors should employ sector-selective approaches rather than uniform momentum strategies across all ETFs, concentrating capital in sectors where overnight momentum effects are strongest (Energy, Utilities, Industrials) while potentially avoiding or modifying approaches in sectors where momentum effects are weaker (Consumer Staples) or where secular trends favor buy-and-hold approaches (Consumer Discretionary in strong economic environments).

Future research directions will focus on incorporating other models of transaction costs and analyzing similar strategies for other asset classes, such as fixed income, commodities, cryptocurrencies, individual stocks, and foreign exchange markets, in order to assess the universality or limitations of the observed temporal patterns and momentum effects across asset classes.

Temporal Decomposition as the Source of Alpha: 24 h Strategy Comparison

A critical question for interpreting the results is whether the outperformance of strategies such as (Long, Reversal) arises from the momentum or reversal signal logic itself, or from the act of decomposing the 24-h period into overnight and daytime sub-periods. We answer this question directly by constructing a matched set of strategies that apply identical momentum and reversal signals to the undivided close-to-close ($R^{CC}$) return, without any sub-period decomposition, and comparing the resulting final portfolio values with those of the sub-period strategies.

Specifically, we define four close-to-close (“CC”) strategies: (i) CC-Momentum Long/Cash, which goes long today if yesterday’s 24-h return was non-negative and otherwise holds cash; (ii) CC-Reversal Long/Cash, which goes long today if yesterday’s return was negative and holds cash otherwise; (iii) CC-Momentum Long/Short, the corresponding long/short variant; and (iv) CC-Reversal Long/Short. These strategies have the same trading frequency as Strategies #1 and #18, use the same signal direction, and are estimated on the same 1999–2025 sample.

Table 19. Average final portfolio value ($100 initial) across all 10 ETFs: sub-period vs. 24-h strategies.

Strategy	0 bps	1 bp	2 bps	3 bps	5 bps
Reference sub-period strategies
(Long, Long)—Buy & Hold	519	519	519	519	519
(Long, Cash)	1022	1022	1022	1022	1022
(Long, Reversal)	61,385	30,539	15,192	7557	1870
(Reversal, Reversal)	20,536	5121	1276	318	20
24 h (close-to-close) strategies using identical signals
CC Momentum Long/Cash	126	90	64	45	23
CC Reversal Long/Cash	602	426	300	212	106
CC Momentum Long/Short	18	9	5	2	0
CC Reversal Long/Short	758	374	185	91	22

reports the average final portfolio value (starting at $100) across all ten ETFs at transaction costs of 0, 1, 2, 3, and 5 basis points, juxtaposing the CC strategies against (Long, Long) (buy-and-hold), (Long, Cash), (Long, Reversal), and (Reversal, Reversal) for reference.

The comparison is unambiguous. The best 24 h strategy, CC-Reversal Long/Short, achieves only $758 at zero costs — approximately $80\times$ less than (Long, Reversal)’s $61,385 and $14\times$ less than even the simple (Long, Cash) strategy. CC-Reversal Long/Cash achieves $602, barely above buy-and-hold’s $519, and below (Long, Cash). The momentum CC strategies perform below buy-and-hold at every cost level.

This result constitutes a direct falsification test: the reversal signal itself, when applied to undivided close-to-close returns, generates negligible additional value beyond a passive buy-and-hold. The enormous outperformance documented for Strategy #18 throughout this paper is therefore attributable to the temporal decomposition of the 24 h period into distinct overnight and daytime sub-periods, rather than to the specific direction of the conditioning signal. The structural asymmetry between overnight returns (persistent positive drift, low volatility, fat tails) and daytime returns (near-zero drift, higher volatility) is the economic substrate that makes sub-period strategies profitable. Applying any signal to the undivided composite return averages away this asymmetry, producing far weaker results. Additional statistical tests to support this are presented in Appendix I.